Arithmetic and Geometric Sequences

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

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What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that is added or subtracted to get from one term to the next in an arithmetic sequence.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply to get from one term to the next in a geometric sequence.

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How do you find the nth term of an arithmetic sequence?

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The nth term can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

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How do you find the nth term of a geometric sequence?

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The nth term can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

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What is the formula to find the sum of the first n terms of an arithmetic sequence?

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The sum S_n of the first n terms can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

What is the formula to find the sum of the first n terms of a geometric sequence?

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The sum S_n of the first n terms can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), for r ≠ 1.

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If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term?

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The 10th term is 32.

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If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 5th term?

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The 5th term is 162.