Practice Explicit and Recursive Sequences

Given the rule:  a_n = 7(½)^n-1
Identify the common ratio.

• a_n

• 7

• ½

• n-1

Given the geometric sequence with a common ratio of ⅓ and the fifth term is 54, find the first term.

• 162

• 486

• 4374

• ⅔

Given a geometric sequence where a₃ = 320 and a₆ = 20480, find a₈

• 4

• 20

• 16,384

• 327,680

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

• 4

• -4

• ¼

• -¼

Which of the following is the correct explicit formula for the geometric sequence shown in the table?

• a_n = 8(1/2)ⁿ

• a_n = 4(2)ⁿ

• a_n = 8(2)ⁿ

• a_n = 4(1/2)ⁿ

Write an explicit equation given a₀ = 5 and r = 2.

• a_n = 5 - 2(n)

• a_n = 2(5)ⁿ

• a_n = 5 + 2(n)

• a_n = 5(2)ⁿ

• r = 4

• r = -3

• r = 1/4

• r = 3

Given the explicit formula a_n = 1(4)ⁿ
Find a₇

Given the explicit formula a_n = 9(1/3)ⁿ
What is the start, a₀ ?

• a₀ = 1/3

• a₀ = 9

• a₀ = 1/9

• a₀ = 3

What is the recursive formula for the geometric sequence shown in the table?

• a_n+1 = a_n + 7
  a₀ = 2

• a_n+1 = a_n + 2
  a₀ = 7