Geometric Sequences

Determine whether the sequence is arithmetic, geometric, or neither.

• arithmetic

• geometric

• neither

Find the common ratio for the geometric sequence.

• 1

• -1

• 7

• -7

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

• r = -8

• r = -1/4

• r = -4

• r = 4

Find the common ratio for the geometric sequence.

• -4

• 4

• 1/4

• -1/4

Write the explicit formula for the following geometric sequence: 10, 20, 40, 80, ...

• a_n = 10(2)^n-1

• a_n = 2(10)^n-1

• a_n = 10(2)ⁿ

• a_n = 2(10)ⁿ

Write the explicit formula for the following geometric sequence: 3, -12, 48, -192, ...

• a_n = 4(3)^n-1

• a_n = 3(4)^n-1

• a_n = -4(3)^n-1

• a_n = 3(-4)^n-1

Find a₁₁ in the following geometric sequence:

• -4,096

• -¹/₂₅₆

• -3,072

• -236,196

Write an explicit rule for the general term of the sequence 5, 15, 45, . . . ?

• a_n = a_n-1 x 3

• a_n = 5(3)^n-1

• a_n = 3(5)^n-1

• a_n = 5 + (n-1)3

Write the explicit rule for the following geometric sequence:

• a_n = 72(-6)^n-1

• a_n = 2(-6)^n-1

• a_n = 2(6)^n-1

• a_n = 72(-6)^n-1

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

• 20, 100, 500, 2500

• 5, 20, 80, 320

• 4, 20, 100, 500

• 4, 9, 14, 19