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

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

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Q. If f(1)=2 f(1)=2 and f(n)=4f(n−1)+n f(n)=4 f(n-1)+n then find the value of f(4) f(4) .\newlineAnswer:
  1. Find f(2)f(2): We are given f(1)=2f(1) = 2. To find f(4)f(4), we need to find the values of f(2)f(2), f(3)f(3), and then f(4)f(4) using the recursive formula f(n)=4f(n−1)+nf(n) = 4f(n-1) + n.\newlineFirst, let's find f(2)f(2) using f(1)f(1).\newlinef(2)=4f(1)+2f(2) = 4f(1) + 2\newlinef(1)=2f(1) = 200\newlinef(1)=2f(1) = 211\newlinef(1)=2f(1) = 222
  2. Find f(3)f(3): Now, let's find f(3)f(3) using f(2)f(2).
    f(3)=4f(2)+3f(3) = 4f(2) + 3
    f(3)=4(10)+3f(3) = 4(10) + 3
    f(3)=40+3f(3) = 40 + 3
    f(3)=43f(3) = 43
  3. Find f(4)f(4): Finally, we can find f(4)f(4) using f(3)f(3).
    f(4)=4f(3)+4f(4) = 4f(3) + 4
    f(4)=4(43)+4f(4) = 4(43) + 4
    f(4)=172+4f(4) = 172 + 4
    f(4)=176f(4) = 176

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