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

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

Back

The common ratio (r) can be found by dividing any term by the previous term: r = a_n / a_(n-1).

Front

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

Back

The nth term of a geometric sequence 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 recursive formula for a geometric sequence?

Back

The recursive formula for a geometric sequence is: a_n = a_(n-1) * r.

Front

Find the 12th term of the geometric sequence: -1, -3, -9, -27, ...

Back

The 12th term a_12 is -177,147.

Front

What is the common ratio of the sequence: 64, -32, 16, -8, ...?

Back

The common ratio is -1/2.

Front

What are the next three terms in the sequence: 512, 256, 128, ...?

Back

The next three terms are 64, 32, 16.

Front

How do you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio between consecutive terms is constant.

Front

What is the first term of the geometric sequence: 5, 15, 45, ...?

Back

The first term a_1 is 5.

Front

If the first term of a geometric sequence is 3 and the common ratio is 4, what is the 5th term?

Back

The 5th term a_5 is 3 * 4^(5-1) = 768.