Question

If a sequence is recursively defined by f(0)=5 and f(n+1)=-4f(n)+2 for n greater than or equal to 0. Find f(3) ?

Answer 1

The correct answer is f(3) = -294

Explanation:

To find f(3), we have to find f(1) and f(2)

It is given that,

f(0)=5 and f(n+1)=-4f(n)+2

To find f(1)

using given information,

f(1) = -4f(0) + 2 = -4*5 + 2 = -20 +2 = -18

To find f(2)

f(2) = -4f(1) + 2 = -4*-18 + 2 = 72 + 2 = 74

To find f(3)

f(3) =-4f(2) + 2 = -4*74 + 2 =-296 + 2 = -294

Therefore the value of f(3) = -294