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If f(1)=8 and f(n+1)=4f(n)-2 then find the value of f(4). Answer:

If f(1)=8 f(1)=8 and f(n+1)=4f(n)−2 f(n+1)=4 f(n)-2 then find the value of f(4) f(4) .\newlineAnswer:

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Q. If f(1)=8 f(1)=8 and f(n+1)=4f(n)−2 f(n+1)=4 f(n)-2 then find the value of f(4) f(4) .\newlineAnswer:
  1. Find f(2)f(2): We are given that f(1)=8f(1) = 8. We need to find f(4)f(4) using the recursive formula f(n+1)=4f(n)−2f(n+1) = 4f(n) - 2. Let's start by finding f(2)f(2).\newlinef(2)=4f(1)−2f(2) = 4f(1) - 2\newlinef(2)=4(8)−2f(2) = 4(8) - 2\newlinef(2)=32−2f(2) = 32 - 2\newlinef(2)=30f(2) = 30
  2. Find f(3)f(3): Now that we have f(2)f(2), we can find f(3)f(3) using the same recursive formula.\newlinef(3)=4f(2)−2f(3) = 4f(2) - 2\newlinef(3)=4(30)−2f(3) = 4(30) - 2\newlinef(3)=120−2f(3) = 120 - 2\newlinef(3)=118f(3) = 118
  3. Find f(4)f(4): Finally, we can find f(4)f(4) using the value of f(3)f(3) we just calculated.\newlinef(4)=4f(3)−2f(4) = 4f(3) - 2\newlinef(4)=4(118)−2f(4) = 4(118) - 2\newlinef(4)=472−2f(4) = 472 - 2\newlinef(4)=470f(4) = 470

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