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. This difference is called the common difference.

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 formula for the nth term of an arithmetic sequence?

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The formula is a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.

Front

What is the formula for the nth term of a geometric sequence?

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The formula is a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.

Front

How do you find the common difference in an arithmetic sequence?

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The common difference (d) is found by subtracting any term from the subsequent term: d = a_(n+1) - a_n.

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How do you find the common ratio in a geometric sequence?

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The common ratio (r) is found by dividing any term by the previous term: r = a_(n+1) / a_n.

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What is the next term in the arithmetic sequence 3, 7, 11, 15?

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The next term is 19.

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What is the next term in the geometric sequence 2, 6, 18, 54?

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The next term is 162.

Front

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

Back

The 10th term is 32.

Front

If the first term of a geometric sequence is 4 and the common ratio is 2, what is the 6th term?

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The 6th term is 128.