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 the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence.

Front

Write a recursive rule for the arithmetic sequence 5, 8, 11, 14...

Back

a_n = a_{n-1} + 3, a_1 = 5.

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

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in a geometric sequence.

Front

Identify the type of sequence: 2, 4, 8, 16...

Back

Geometric.

Front

Identify the type of sequence: 10, 7, 4, 1...

Back

Arithmetic.

Front

Find the first four terms of the sequence given the rule: a_n = 3(2)^(n-1)

Back

3, 6, 12, 24.

Front

Find the next three terms for the geometric sequence: 3, 9, 27...

Back

81, 243, 729.

Front

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

Back

a_n = a_1 + (n-1)d, where d is the common difference.