Question

Look at the pattern shown below.

2, 4, 16, 256 ...

What is f(n+ 1) in terms of f(n), where n represents the position of a term in this pattern?

A. (F(n))^2

B. 2(f(n))

C. (F(n)-1)^2

D. 2(f(n)-1)

Answer 1

Answer: (a)

Explanation:

Given

The pattern is 2, 4, 16, 256...

From the pattern, we can see that the next term is square of the previous i.e.

`\Rightarrow 4=2^2\\\Rightarrow 16=4^2\\\Rightarrow 256=16^2`
`\Rightarrow 4=2^2\\\Rightarrow 16=4^2\\\Rightarrow 256=16^2`

So, for the
`n^(th)` term, the function is
`f(n)`

For the next term, it is
`f(n+1)`

So,

`\Rightarrow f(n+1)=[f(n)]^2`