Geometric Sequences

Front

What does r represent in a geometric sequence?

Back

Common ratio

Front

Find the common ratio for the geometric sequence: 2, 4, 8, 16, ...

Back

r = 2

Front

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

Back

r = 2

Front

Find the common ratio for the geometric sequence: 5, 15, 45, 135, ...

Back

r = 3

Front

Find the common ratio for the geometric sequence: 10, 5, 2.5, 1.25, ...

Back

r = 1/2

Front

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

Back

r = -2

Front

Find the common ratio for the geometric sequence: 64, -16, 4, -1, ...

Back

r = -1/4

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 3 and the common ratio is 4, what is the 5th term?

Back

a_5 = 3 * 4^(5-1) = 768

Front

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

Back

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