1.2.2 Identifying 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).

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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 find the common difference in an arithmetic sequence?

Back

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

Front

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

Back

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

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

Back

The nth term (a_n) of an arithmetic sequence can be calculated using the formula: 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 nth term (a_n) of a geometric sequence can be calculated 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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Identify the common difference in the sequence: 5, 8, 11, 14...

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The common difference (d) is 3.

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

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The common ratio (r) is 2.

Front

Is the sequence 2, 4, 8, 16... arithmetic, geometric, or neither?

Back

The sequence is geometric.

Front

Is the sequence 10, 20, 30, 40... arithmetic, geometric, or neither?

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The sequence is arithmetic.