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?

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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.

Front

How do you find the nth term of an arithmetic sequence?

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Front

How do you find the nth term of a geometric sequence?

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Front

What is the common difference in the sequence 2, 5, 8, 11, ...?

Back

The common difference is 3, as each term increases by 3.

Front

What is the common ratio in the sequence 3, 6, 12, 24, ...?

Back

The common ratio is 2, as each term is multiplied by 2 to get the next term.

Front

Identify whether the sequence 4, 8, 16, 32, ... is arithmetic, geometric, or neither.

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The sequence is geometric with a common ratio of 2.

Front

Identify whether the sequence 10, 7, 4, 1, ... is arithmetic, geometric, or neither.

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The sequence is arithmetic with a common difference of -3.

Front

What is the explicit formula for the arithmetic sequence 3, 7, 11, 15, ...?

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Front

What is the explicit formula for the geometric sequence 2, 6, 18, 54, ...?

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