Question

Which formula defines a sequence
$f(1) = 2$
$f(2) = 6$
$f(3) = 10$
$f(4) = 14$
$f(5) = 18$

Answer 1

Given:

Values of function at some points is

$f(1)=2,f(2)=6,f(3)=10,f(4)=14,f(5)=18$

Required:

We will find sequence corresponding given condition.

Explanation:

We will check by options

In option 2 we can check the values

$\begin{gathered} f(1)=2,f(n)=4+f(n-1)\text{ }for\text{ }n\ge2 \\ At\text{ }x=2 \\ f(2)=4+f(1) \\ f(2)=4+2 \\ f(2)=6 \\ At\text{ x=3} \\ f(3)=4+6 \\ f(3)=10 \\ At\text{ x=4} \\ f(4)=4+10 \\ f(4)=14 \\ At\text{ x=5} \\ f(5)=4+14 \\ f(5)=18 \end{gathered}$

Answer:

Hence, sequence in option B is correct.