9.3 Arithmetic and Geometric Sequences Review

Front

What is a geometric sequence?

Back

A sequence 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 an arithmetic sequence?

Back

A sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.

Front

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

Back

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

Front

What is the formula for the nth term of a geometric sequence?

Back

a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

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

Back

Divide any term by the previous term (r = a_n / a_(n-1)).

Front

If a geometric sequence has a common ratio of 5, what are the first three terms if the first term is 2?

Back

2, 10, 50.

Front

What is the common difference in the arithmetic sequence 4, 7, 10, 13?

Back

3.

Front

Find the 10th term of the arithmetic sequence: 5, 8, 11, 14...

Back

32.

Front

What is the 5th term of the geometric sequence: 3, 9, 27, 81...?

Back

243.

Front

If a_3 = 12 and a_6 = 96 in a geometric sequence, what is the common ratio?

Back

2.