Question

1. Which formula defines the sequence f(1)=2, f(2)= 6, f(3)= 10, f(4)= 14, f(5)= 18?

A. 101- 2. f(n)= 6 + f(n-1) for n> 2
B. f(1)= 2, f(n)= 4 fln-1) for n> 2
C. f(1)= 2, f(n)= 2 + f(n-1) for n 2
D. f(1)= 6, f(n)= 4 + f(n-1) for n> 2
А
B
С
D

Answer 1

`f(n) =4 + f(n-1) \\for\ n>2`

Explanation:

Given

`f(1)=2\\ f(2)= 6\\ f(3)= 10\\ f(4)= 14\\ f(5)= 18`

Required

Determine the formula

First, we need to solve common difference (d)

`d = f(n) - f(n-1)`

Take n as 2

`d = f(2) - f(2-1)`

`d = 6 - 2`

`d = 4`

Represent each function as a sum of the previous

`f(1) = 2`

`f(2) = 2 + 4 = f(1) + 4`

`f(3) = 6 + 4 = f(2) + 4`

`f(4) = 10 + 4 = f(3) + 4`

`f(5) = 14 + 4 = f(4) + 4`

Represent the function as
`f(n)`

`f(n) =f(n-1) + 4`

Reorder

`f(n) =4 + f(n-1) \\for\ n>2`