Question

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

Answer 1

Answer:

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

Step-by-step 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

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