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If 
f(1)=7 and 
f(n)=2f(n-1)-2 then find the value of 
f(3).
Answer:

If f(1)=7 f(1)=7 and f(n)=2f(n1)2 f(n)=2 f(n-1)-2 then find the value of f(3) f(3) .\newlineAnswer:

Full solution

Q. If f(1)=7 f(1)=7 and f(n)=2f(n1)2 f(n)=2 f(n-1)-2 then find the value of f(3) f(3) .\newlineAnswer:
  1. Find f(2)f(2): We are given the initial condition f(1)=7f(1) = 7 and the recursive formula f(n)=2f(n1)2f(n) = 2f(n-1) - 2. To find f(3)f(3), we first need to find f(2)f(2) using the recursive formula.\newlineUsing the formula, we substitute n=2n = 2 to find f(2)f(2):\newlinef(2)=2f(21)2f(2) = 2f(2-1) - 2\newlinef(2)=2f(1)2f(2) = 2f(1) - 2\newlinef(2)=2×72f(2) = 2 \times 7 - 2\newlinef(1)=7f(1) = 700\newlinef(1)=7f(1) = 711
  2. Find f(3)f(3): Now that we have f(2)f(2), we can use it to find f(3)f(3) using the same recursive formula.\newlineSubstitute n=3n = 3 into the formula to find f(3)f(3):\newlinef(3)=2f(31)2f(3) = 2f(3-1) - 2\newlinef(3)=2f(2)2f(3) = 2f(2) - 2\newlinef(3)=2×122f(3) = 2 \times 12 - 2\newlinef(3)=242f(3) = 24 - 2\newlinef(3)=22f(3) = 22

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