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If f(1) = 4 and f(n)=-4f(n -1) then find the value of f(4)

User Zamnuts
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Answer:

f(4) = 256

Explanation:

f(1) = 4

f(n) = 4f(n-1)

f(2) = 4 f(1) = 4 x 4 = 16

f(3) = 4 f(2) = 4 x 16 = 64

f(4) = 4 f(3) = 4 x 64 = 256

The general formula is f(n) = 4ⁿ

This is a geometric progression with first term 4 and common ratio 4 so it is usual to write this as

f(n) = a₁ · 4ⁿ⁻¹

with a₁ the first term = 4

So f(n) = 4 x 4ⁿ⁻¹

(which is the same as 4ⁿ

User Derekdreery
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