Question

Which sequence matches the recursive formula?

an = (an-1)2 + 3, where a1 = 2

A)
2, 4, 16, 256, ...


B)
2, 7, 17, 37, ...


C)
2, 7, 52, 2707, ...


D)
2, 25, 784, 6159, ...

Answer 1

The solution is 2, 7, 52, 2707, .... To find each term in the sequence, you square the previous term and add 3. This sequence is represented by the recursive formula an = (an-1)2 + 3, where a1 = 2.

So It's C.

Explanation:

Answer 2

a1 = 2
a2 = (a1)^2 + 3 = 2^2 + 3 = 4 + 3 = 7
a3 = (a2)^2 + 3 = 7^2 + 3 = 49 + 3 = 52
a4 = (a3)^2 + 3 = 52^2 + 3 = 2,704 + 3 = 2,707

Option C is the correct answer.