ai-anytime/distilabel-math-instructions · Datasets at Hugging Face

instructions stringlengths 34 238
"Can you explain the concept of geometric progressions and provide an example?"
"What is the formula to find the nth term of a geometric progression?"
"Please outline the steps to determine the sum of a geometric progression."
"Detail the process of finding the common ratio in a given geometric progression."
How can I find the common ratio in a geometric progression?
Please explain the formula to calculate the nth term of a geometric progression.
Detail the process of finding the sum of an infinite geometric progression.
Can you provide an example of a real-life scenario where geometric progressions are used?
"Explain the concept of geometric progressions and provide an example."
"How do you find the common ratio in a geometric progression?"
"Detail the process of determining the nth term in a geometric progression."
"What is the significance of the sum of a geometric progression?"
"Explain the concept of geometric progressions and provide an example."
"What are the applications of geometric progressions in real-life scenarios?"
"Detail the steps to find the nth term of a geometric progression."
"Solve the following geometric progression problem: Find the sum of the first 5 terms with a common ratio of 3 and a first term of 2."
What is the formula to find the nth term of a geometric progression?
Explain the concept of common ratio in geometric progressions.
Can you provide step-by-step instructions on how to find the sum of the first n terms of a geometric progression?
Detail the process of determining whether a given sequence is a geometric progression or not.
How can I find the sum of the first 10 terms in a geometric progression?
What is the formula to calculate the nth term of a geometric progression?
Can you explain the concept of common ratio in geometric progressions?
Please detail the process of finding the sum of an infinite geometric progression.
How can I find the nth term of a geometric progression?
Provide a step-by-step explanation of how to sum the terms of a geometric progression.
Explain the concept of a common ratio in geometric progressions.
What is the significance of the first term in a geometric progression?
What is the formula for finding the nth term of a geometric progression?
Explain how to determine if a given sequence is a geometric progression.
Could you outline the steps to find the sum of the first n terms of a geometric progression?
Detail the process of finding the common ratio of a geometric progression.
How can I find the common ratio of a geometric progression?
Please explain the formula to calculate the nth term of a geometric progression.
What is the significance of the sum of an infinite geometric progression?
Could you outline the steps to find the sum of the first n terms of a geometric progression?
What is the formula to find the nth term of a geometric progression?
Explain the concept of common ratio in a geometric progression.
Can you provide a real-life example of a geometric progression and explain its significance?
Detail the steps to find the sum of a finite geometric progression.
How can harmonic progressions be defined in the context of music theory?
Explain the significance of harmonic progressions in composing a musical piece.
Provide step-by-step instructions on how to identify harmonic progressions in a given musical score.
What are the different types of harmonic progressions commonly used in classical music compositions?
What are the properties of a harmonic progression and how can they be applied to solve math problems?
Explain the concept of harmonic progression and give an example where it can be used to solve a real-life scenario.
Detail the steps involved in finding the nth term of a harmonic progression and provide an example to illustrate the process.
Can you demonstrate how to find the sum of the first n terms of a harmonic progression? Please provide a step-by-step explanation.
"Explain the concept of harmonic progressions and provide an example."
"What are the properties of harmonic progressions and how are they different from arithmetic progressions?"
"Solve the following harmonic progression: 1/2, 1/4, 1/8, ..."
"Detail the steps to find the nth term of a harmonic progression."
What are the properties of a harmonic progression and how can they be identified in a given sequence of numbers?
Describe the process of finding the n-th term of a harmonic progression given the first term and the common difference.
Can you explain the concept of harmonic progression using a real-life scenario or example?
Outline the steps to determine the sum of the first n terms of a harmonic progression.
What are the properties of a harmonic progression and how can they be used in real-life scenarios involving math and reasoning?
Provide a step-by-step explanation of how to find the nth term of a harmonic progression.
Detail the process of determining if a given sequence is a harmonic progression or not.
Explain the significance of harmonic progressions in music theory and how they are used to create musical compositions.
How can harmonic progressions be defined and explained in music theory?
Provide the step-by-step process of constructing a harmonic progression in the key of C major.
What is the significance of harmonic progressions in creating a sense of tension and resolution in music?
Detail the application of harmonic progressions in jazz improvisation and chord substitutions.
Explain the concept of harmonic progressions and provide an example.
What are the properties of a harmonic progression?
Detail the steps to find the nth term in a harmonic progression.
Can you solve a real-life problem using harmonic progressions? If so, please provide an example.
Explain the concept of harmonic progressions and provide an example.
What are the different types of harmonic progressions and how do they differ from each other?
Calculate the next term in the harmonic progression: 1, 1/2, 1/3, 1/4, ...
Detail the process of finding the sum of an infinite harmonic progression.
What are the properties of a harmonic progression?
Explain the concept of harmonic progression and its applications in real-life scenarios.
Can you outline the steps to find the nth term of a harmonic progression?
Detail the process of determining the sum of a finite harmonic progression.
What are the properties of a harmonic progression and how does it differ from an arithmetic progression?
Can you explain the concept of harmonic mean and how it relates to harmonic progressions?
Detail the process of finding the nth term of a harmonic progression and provide an example.
What is the significance of harmonic progressions in music theory and how are they used?
What are the trigonometric ratios and how are they used in solving mathematical problems involving angles?
Explain the process of finding the sine, cosine, and tangent ratios of an angle in trigonometry.
Can you provide a step-by-step solution to finding the value of a missing angle using trigonometric ratios?
Detail the significance of trigonometric ratios in real-life scenarios, such as architecture or navigation.
Determine the sine value of angle A in a right triangle with a hypotenuse of 10 units and an adjacent side of 6 units.
Explain the process of calculating the tangent ratio for an angle in a right triangle given the length of the opposite side and the adjacent side.
What is the significance of the cosine ratio in trigonometry and how is it used to solve problems involving right triangles?
Could you outline the steps to find the missing side length in a right triangle using the Pythagorean theorem?
"Explain how to find the sine of an angle in trigonometry and provide an example."
"What are the steps to determine the cosine of an angle in trigonometry? Can you demonstrate with an example?"
"Detail the process of calculating the tangent of an angle in trigonometry and provide a practical application."
"How can I determine the cosecant of an angle in trigonometry? Please provide an example."
"Can you explain how to calculate the sine of an angle?"
"What is the process for finding the cosine of an angle?"
"Detail the steps to determine the tangent of an angle."
"Could you elucidate the procedure for evaluating the cosecant of an angle?"
"Explain the process of finding the sine of an angle in a right triangle."
"What is the significance of the cosine function in trigonometry?"
"Detail the steps involved in calculating the tangent of an angle."
"Can you provide a step-by-step solution for finding the value of the sine function for a given angle?"

"Can you explain the concept of geometric progressions and provide an example?"

"What is the formula to find the nth term of a geometric progression?"

"Please outline the steps to determine the sum of a geometric progression."

"Detail the process of finding the common ratio in a given geometric progression."

How can I find the common ratio in a geometric progression?

Please explain the formula to calculate the nth term of a geometric progression.

Detail the process of finding the sum of an infinite geometric progression.

Can you provide an example of a real-life scenario where geometric progressions are used?

"Explain the concept of geometric progressions and provide an example."

"How do you find the common ratio in a geometric progression?"

"Detail the process of determining the nth term in a geometric progression."

"What is the significance of the sum of a geometric progression?"

"Explain the concept of geometric progressions and provide an example."

"What are the applications of geometric progressions in real-life scenarios?"

"Detail the steps to find the nth term of a geometric progression."

"Solve the following geometric progression problem: Find the sum of the first 5 terms with a common ratio of 3 and a first term of 2."

What is the formula to find the nth term of a geometric progression?

Explain the concept of common ratio in geometric progressions.

Can you provide step-by-step instructions on how to find the sum of the first n terms of a geometric progression?

Detail the process of determining whether a given sequence is a geometric progression or not.

How can I find the sum of the first 10 terms in a geometric progression?

What is the formula to calculate the nth term of a geometric progression?

Can you explain the concept of common ratio in geometric progressions?

Please detail the process of finding the sum of an infinite geometric progression.

How can I find the nth term of a geometric progression?

Provide a step-by-step explanation of how to sum the terms of a geometric progression.

Explain the concept of a common ratio in geometric progressions.

What is the significance of the first term in a geometric progression?

What is the formula for finding the nth term of a geometric progression?

Explain how to determine if a given sequence is a geometric progression.

Could you outline the steps to find the sum of the first n terms of a geometric progression?

Detail the process of finding the common ratio of a geometric progression.

How can I find the common ratio of a geometric progression?

Please explain the formula to calculate the nth term of a geometric progression.

What is the significance of the sum of an infinite geometric progression?

Could you outline the steps to find the sum of the first n terms of a geometric progression?

What is the formula to find the nth term of a geometric progression?

Explain the concept of common ratio in a geometric progression.

Can you provide a real-life example of a geometric progression and explain its significance?

Detail the steps to find the sum of a finite geometric progression.

How can harmonic progressions be defined in the context of music theory?

Explain the significance of harmonic progressions in composing a musical piece.

Provide step-by-step instructions on how to identify harmonic progressions in a given musical score.

What are the different types of harmonic progressions commonly used in classical music compositions?

What are the properties of a harmonic progression and how can they be applied to solve math problems?

Explain the concept of harmonic progression and give an example where it can be used to solve a real-life scenario.

Detail the steps involved in finding the nth term of a harmonic progression and provide an example to illustrate the process.

Can you demonstrate how to find the sum of the first n terms of a harmonic progression? Please provide a step-by-step explanation.

"Explain the concept of harmonic progressions and provide an example."

"What are the properties of harmonic progressions and how are they different from arithmetic progressions?"

"Solve the following harmonic progression: 1/2, 1/4, 1/8, ..."

"Detail the steps to find the nth term of a harmonic progression."

What are the properties of a harmonic progression and how can they be identified in a given sequence of numbers?

Describe the process of finding the n-th term of a harmonic progression given the first term and the common difference.

Can you explain the concept of harmonic progression using a real-life scenario or example?

Outline the steps to determine the sum of the first n terms of a harmonic progression.

What are the properties of a harmonic progression and how can they be used in real-life scenarios involving math and reasoning?

Provide a step-by-step explanation of how to find the nth term of a harmonic progression.

Detail the process of determining if a given sequence is a harmonic progression or not.

Explain the significance of harmonic progressions in music theory and how they are used to create musical compositions.

How can harmonic progressions be defined and explained in music theory?

Provide the step-by-step process of constructing a harmonic progression in the key of C major.

What is the significance of harmonic progressions in creating a sense of tension and resolution in music?

Detail the application of harmonic progressions in jazz improvisation and chord substitutions.

Explain the concept of harmonic progressions and provide an example.

What are the properties of a harmonic progression?

Detail the steps to find the nth term in a harmonic progression.

Can you solve a real-life problem using harmonic progressions? If so, please provide an example.

Explain the concept of harmonic progressions and provide an example.

What are the different types of harmonic progressions and how do they differ from each other?

Calculate the next term in the harmonic progression: 1, 1/2, 1/3, 1/4, ...

Detail the process of finding the sum of an infinite harmonic progression.

What are the properties of a harmonic progression?

Explain the concept of harmonic progression and its applications in real-life scenarios.

Can you outline the steps to find the nth term of a harmonic progression?

Detail the process of determining the sum of a finite harmonic progression.

What are the properties of a harmonic progression and how does it differ from an arithmetic progression?

Can you explain the concept of harmonic mean and how it relates to harmonic progressions?

Detail the process of finding the nth term of a harmonic progression and provide an example.

What is the significance of harmonic progressions in music theory and how are they used?

What are the trigonometric ratios and how are they used in solving mathematical problems involving angles?

Explain the process of finding the sine, cosine, and tangent ratios of an angle in trigonometry.

Can you provide a step-by-step solution to finding the value of a missing angle using trigonometric ratios?

Detail the significance of trigonometric ratios in real-life scenarios, such as architecture or navigation.

Determine the sine value of angle A in a right triangle with a hypotenuse of 10 units and an adjacent side of 6 units.

Explain the process of calculating the tangent ratio for an angle in a right triangle given the length of the opposite side and the adjacent side.

What is the significance of the cosine ratio in trigonometry and how is it used to solve problems involving right triangles?

Could you outline the steps to find the missing side length in a right triangle using the Pythagorean theorem?

"Explain how to find the sine of an angle in trigonometry and provide an example."

"What are the steps to determine the cosine of an angle in trigonometry? Can you demonstrate with an example?"

"Detail the process of calculating the tangent of an angle in trigonometry and provide a practical application."

"How can I determine the cosecant of an angle in trigonometry? Please provide an example."

"Can you explain how to calculate the sine of an angle?"

"What is the process for finding the cosine of an angle?"

"Detail the steps to determine the tangent of an angle."

"Could you elucidate the procedure for evaluating the cosecant of an angle?"

"Explain the process of finding the sine of an angle in a right triangle."

"What is the significance of the cosine function in trigonometry?"

"Detail the steps involved in calculating the tangent of an angle."

"Can you provide a step-by-step solution for finding the value of the sine function for a given angle?"