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

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.

Step-by-step 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.