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If f(1)=1 and f(n)=5f(n-1)+3 then find the value of f(3). Answer:

If f(1)=1 f(1)=1 and f(n)=5f(n−1)+3 f(n)=5 f(n-1)+3 then find the value of f(3) f(3) .\newlineAnswer:

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Q. If f(1)=1 f(1)=1 and f(n)=5f(n−1)+3 f(n)=5 f(n-1)+3 then find the value of f(3) f(3) .\newlineAnswer:
  1. Find f(2)f(2): We are given the initial condition f(1)=1f(1) = 1. To find f(3)f(3), we first need to find f(2)f(2) using the recursive formula f(n)=5f(n−1)+3f(n) = 5f(n-1) + 3.\newlineCalculation: f(2)=5f(2−1)+3=5f(1)+3=5(1)+3=5+3=8f(2) = 5f(2-1) + 3 = 5f(1) + 3 = 5(1) + 3 = 5 + 3 = 8.
  2. Use f(2)f(2) to 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.\newlineCalculation: f(3)=5f(3−1)+3=5f(2)+3=5(8)+3=40+3=43f(3) = 5f(3-1) + 3 = 5f(2) + 3 = 5(8) + 3 = 40 + 3 = 43.

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