Geometric Sequences

Front

What does r represent in a geometric sequence?

Back

Common ratio

Front

Find the common ratio for the geometric sequence: 3, 6, 12, 24,...

Back

r = 2

Front

Determine whether the sequence 5, 10, 20, 40,... is arithmetic, geometric, or neither.

Back

geometric

Front

Find the common ratio for the sequence: 8, 4, 2, 1,...

Back

r = 1/2

Front

Is the sequence 1, 3, 9, 27,... geometric?

Back

yes

Front

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

Back

a_n = a_1 * r^(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

a_4 = 5 * 3^(4-1) = 135

Front

Identify the common ratio in the sequence: 16, 8, 4, 2,...

Back

r = 1/2

Front

What is the sum of the first n terms of a geometric series?

Back

S_n = a_1 * (1 - r^n) / (1 - r) if r ≠ 1

Front

If a geometric sequence has a common ratio of -2, what is the 3rd term if the first term is 3?

Back

a_3 = 3 * (-2)^(3-1) = 12