geometric and arithmetic 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.

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 identify an arithmetic sequence?

Back

An arithmetic sequence can be identified by checking if the difference between consecutive terms is the same.

Front

How do you identify a geometric sequence?

Back

A geometric sequence can be identified by checking if the ratio of consecutive terms is constant.

Front

What is the common difference in the sequence 3, 7, 11, 15?

Back

The common difference is 4.

Front

What is the common ratio in the sequence 2, 6, 18, 54?

Back

The common ratio is 3.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula for an arithmetic sequence is a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the explicit formula for a geometric sequence?

Back

The explicit formula for a geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

Calculate a_22 for the sequence defined by a_n = 5 - 3n.

Back

a_22 = -61.

Front

What is a_5 in the sequence defined as a_n = 5 * 2^(n-1)?

Back

a_5 = 80.