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What is a common ratio in a geometric sequence?

Back

The common ratio is the factor by which each term in a geometric sequence is multiplied to get the next term.

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What is the formula to find the nth term of an arithmetic sequence?

Back

The nth term (a_n) 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 calculate the sum of the first n terms of an arithmetic series?

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

Front

What is the formula for the sum of the first n terms of a geometric series?

Back

The sum (S_n) can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), where a_1 is the first term and r is the common ratio.

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What is an arithmetic sequence?

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

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What is a geometric sequence?

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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.

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If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 4th term?

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The 4th term is 2 * 3^(4-1) = 2 * 27 = 54.

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What is the common difference in an arithmetic sequence?

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The common difference is the constant amount that is added to each term to get the next term in an arithmetic sequence.

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How do you find the 32nd term of the sequence 34, 37, 40, 43, ...?

Back

Using the formula for the nth term: a_n = a_1 + (n-1)d, where a_1 = 34 and d = 3, the 32nd term is 34 + (32-1)3 = 34 + 93 = 127.

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What is the sum of the first 10 terms of the series 2 - 6 + 18 - 54 + ...?

Back

The sum is -29524.