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

Determine if the sequence 2, 6, 18, 54 is arithmetic, geometric, or neither.

Back

geometric

Front

What is the next term in the geometric sequence 3, 9, 27?

Back

81

Front

Find the common ratio for the geometric sequence 5, 15, 45.

Back

3

Front

Find the common ratio for the geometric sequence 8, -4, 2.

Back

-1/2

Front

Is the sequence 1, 2, 4, 8, 16 geometric?

Back

yes

Front

What is the next term in the geometric sequence 10, 20, 40?

Back

80

Front

Determine if the sequence 1, 4, 9, 16 is arithmetic, geometric, or neither.

Back

neither

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.