Question

Which recursive formula describes the sequence below? 5,13,29,61,125

Answer 1

Answer:

f(n) = f(n-1) + 8ⁿ⁻¹

Step-by-step explanation:

The series is 5, 13, 29, 61, 125

13 - 5 = 8

29 - 13 = 16

61 - 29 = 32

125 - 61 = 64

Here, f(1) = 5

∴ f(2) = f(1) + 8¹ = 5 + 8 = 13

f(3) = f(2) + 8² = 13 + 16 = 29

f(4) = f(3) + 8³ = 29 + 32 = 61

And so on

∴ f(n) = f(n-1) + 8ⁿ⁻¹