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. For example, 2, 5, 8, 11 is an arithmetic sequence with a common difference of 3.

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. For example, 3, 6, 12, 24 is a geometric sequence with a common ratio of 2.

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How do you find the next term in an arithmetic sequence?

Back

To find the next term in an arithmetic sequence, add the common difference to the last term. For example, in the sequence 4, 7, 10, 13, the next term is 13 + 3 = 16.

Front

How do you find the next term in a geometric sequence?

Back

To find the next term in a geometric sequence, multiply the last term by the common ratio. For example, in the sequence 2, 6, 18, 54, the next term is 54 x 3 = 162.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The formula for the nth term of an arithmetic sequence is a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

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

Back

The formula for the nth term of a geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

Identify the common difference in the sequence: 5, 10, 15, 20.

Back

The common difference is 5, as each term increases by 5.

Front

Identify the common ratio in the sequence: 1, 3, 9, 27.

Back

The common ratio is 3, as each term is multiplied by 3 to get the next term.

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What is the explicit rule for the sequence: 2, 5, 8, 11?

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The explicit rule is a_n = 2 + 3(n-1), where 3 is the common difference.

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What is the explicit rule for the sequence: 4, 12, 36, 108?

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The explicit rule is a_n = 4 * 3^(n-1), where 3 is the common ratio.