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 (d).

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 (r).

Front

How do you determine if a sequence is arithmetic?

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To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant. If it is, the sequence is arithmetic.

Front

How do you determine if a sequence is geometric?

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To determine if a sequence is geometric, check if the ratio of consecutive terms is constant. If it is, the sequence is geometric.

Front

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

Back

Front

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

Back

Front

Find the common difference in the arithmetic sequence: 5, 8, 11, 14.

Back

The common difference (d) is 3, since 8 - 5 = 3, 11 - 8 = 3, and 14 - 11 = 3.

Front

Find the common ratio in the geometric sequence: 3, 6, 12, 24.

Back

The common ratio (r) is 2, since 6/3 = 2, 12/6 = 2, and 24/12 = 2.

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What are the next three terms in the arithmetic sequence: 10, 15, 20, ...?

Back

The next three terms are 25, 30, and 35.

Front

What are the next three terms in the geometric sequence: 2, 6, 18, ...?

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The next three terms are 54, 162, and 486.