Arithmetic and Geometric Sequences Review

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

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

Back

To find the common difference (d), subtract the first term from the second term: d = a2 - a1.

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 find the common ratio in a geometric sequence?

Back

To find the common ratio (r), divide the second term by the first term: r = a2 / a1.

Front

Given the sequence 30, 39, 48, 57, identify a1 and d.

Back

a1 = 30; d = 9.

Front

Find the common difference of the sequence 25, 13, 1, -11.

Back

The common difference is -12.

Front

Which of the following is a geometric sequence? -1, 6, -36, 216 or 2, 4, 6, 8?

Back

-1, 6, -36, 216 is a geometric sequence.

Front

Find the common ratio of the sequence 2, 8, 32, 128.

Back

The common ratio is 4.

Front

What are the first 4 terms of an arithmetic sequence with a common difference of -6 if the first term is 76?

Back

The first 4 terms are 76, 70, 64, 58.

Front

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

Back

The nth term (an) can be calculated using the formula: an = a1 + (n-1)d.