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) ?

Question

Mathematics

Marcel

22 December, 03:10

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) ?

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Answers (1)

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Lawson Gordon · Answer 1

The correct answer is f (3) = - 294

Step-by-step 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