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 a geometric sequence.

Front

Find the next term in the sequence: 3, 9, 27, __.

Back

The next term is 81.

Front

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

Back

The second term is 6.

Front

What is the formula for 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

Determine the common ratio of the sequence: 5, 15, 45, __.

Back

The common ratio is 3.

Front

What is the next term in the sequence: 1, 2, 4, 8, __?

Back

The next term is 16.

Front

If the first term of a geometric sequence is 10 and the third term is 90, what is the common ratio?

Back

The common ratio is 3.

Front

Find the missing term in the geometric sequence: 12, __, 108.

Back

The missing term is 36.

Front

What is the common ratio of the sequence: 8, -32, 128?

Back

The common ratio is -4.