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 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

Find the 11th term for the geometric sequence: 64, -32, 16, -8, ...

Back

The 11th term is -0.0625.

Front

Which formula is used to find the explicit equation for geometric sequences?

Back

The formula is a_n = a_1 * r^(n-1).

Front

Find the next three terms: -4, -12, -36, -108, ...

Back

The next three terms are -324, -972, -2916.

Front

Find the next three terms: 4, 12, 36, 108, ...

Back

The next three terms are 324, 972, 2916.

Front

What is the common ratio in the sequence: 64, -16, 4, -1, ...?

Back

The common ratio is r = -1/4.

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

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

Back

The 4th term is 5 * 3^(4-1) = 5 * 27 = 135.

Front

What is the relationship between the terms in a geometric sequence?

Back

Each term is obtained by multiplying the previous term by the common ratio.