Arithmetic and Geometric Sequence

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

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

Back

The common difference can be found by subtracting any term from the subsequent term. For example, in the sequence 2, 5, 8, the common difference is 5 - 2 = 3.

Front

Is the sequence 17, 9, 1, -7 an arithmetic sequence?

Back

Yes, the common difference is -8.

Front

Is the sequence 78, 785, 7855, 78555 an arithmetic sequence?

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No, the difference between consecutive terms is not constant.

Front

What are the next three terms in the arithmetic sequence: -33, -24, -15, -6?

Back

3, 12, 21.

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

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

Back

The common ratio can be found by dividing any term by the previous term. For example, in the sequence 3, 6, 12, the common ratio is 6 / 3 = 2.

Front

What is the common ratio of the sequence 5, 25, 125?

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The common ratio is 5.

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