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If f(1)=3 and f(n)=4f(n-1)-1 then find the value of f(3). Answer:

If f(1)=3 f(1)=3 and f(n)=4f(n−1)−1 f(n)=4 f(n-1)-1 then find the value of f(3) f(3) .\newlineAnswer:

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Q. If f(1)=3 f(1)=3 and f(n)=4f(n−1)−1 f(n)=4 f(n-1)-1 then find the value of f(3) f(3) .\newlineAnswer:
  1. Find f(2)f(2): We are given that f(1)=3f(1) = 3. To find f(3)f(3), we need to first find f(2)f(2) using the recursive formula f(n)=4f(n−1)−1f(n) = 4f(n-1) - 1. Substitute n=2n = 2 into the formula to find f(2)f(2). f(2)=4f(2−1)−1f(2) = 4f(2-1) - 1 f(2)=4f(1)−1f(2) = 4f(1) - 1 f(2)=4(3)−1f(2) = 4(3) - 1 f(1)=3f(1) = 300 f(1)=3f(1) = 311
  2. Calculate 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)=4f(3−1)−1f(3) = 4f(3-1) - 1\newlinef(3)=4f(2)−1f(3) = 4f(2) - 1\newlinef(3)=4(11)−1f(3) = 4(11) - 1\newlinef(3)=44−1f(3) = 44 - 1\newlinef(3)=43f(3) = 43

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