Geometric Sequences

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 the sequence.

Front

Given the rule: a_n = 7(½)^(n-1), what is the common ratio?

Back

½

Front

Find the next three terms for the geometric sequence: 64, 16, 4,...

Back

1, ¼, 1/16

Front

Given the rule: a_n = 7(½)^(n-1), what is the first term?

Back

7

Front

Find the common ratio for the geometric sequence: 64, 16, 4,...

Back

¼

Front

How do you find the nth term of a geometric sequence?

Back

The nth term can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What is the formula for the sum of the first n terms of a geometric sequence?

Back

The sum S_n of the first n terms is given by S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.

Front

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 5th term?

Back

The 5th term is 3 * 2^(5-1) = 48.

Front

What happens to the terms of a geometric sequence if the common ratio is between 0 and 1?

Back

The terms will decrease and approach zero.