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{d(1)=13 d(n)=d(n−1)+17\begin{cases}d(1)=13\ d(n)=d(n-1)+17 \end{cases}

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Full solution

Q. {d(1)=13 d(n)=d(n−1)+17\begin{cases}d(1)=13\ d(n)=d(n-1)+17 \end{cases}
  1. Base Case: We are given the initial value of the sequence:\newlined(1)=13d(1) = 13\newlineThis is our base case for the recursive sequence.
  2. Recursive Formula: We are also given the recursive formula:\newlined(n)=d(n−1)+17d(n) = d(n-1) + 17\newlineThis means that to find the value of d(n)d(n), we need to add 1717 to the value of d(n−1)d(n-1).
  3. Find d(2)d(2): To find d(2)d(2), we use the recursive formula with n=2n=2:
    d(2)=d(1)+17d(2) = d(1) + 17
    Now we substitute the known value of d(1)d(1):
    d(2)=13+17d(2) = 13 + 17
    d(2)=30d(2) = 30
  4. Find d(3)d(3): To find d(3)d(3), we use the recursive formula with n=3n=3:
    d(3)=d(2)+17d(3) = d(2) + 17
    We substitute the known value of d(2)d(2):
    d(3)=30+17d(3) = 30 + 17
    d(3)=47d(3) = 47
  5. Find d(4)d(4): To find d(4)d(4), we use the recursive formula with n=4n=4:
    d(4)=d(3)+17d(4) = d(3) + 17
    We substitute the known value of d(3)d(3):
    d(4)=47+17d(4) = 47 + 17
    d(4)=64d(4) = 64
  6. Find d(5)d(5): Finally, to find d(5)d(5), we use the recursive formula with n=5n=5:
    d(5)=d(4)+17d(5) = d(4) + 17
    We substitute the known value of d(4)d(4):
    d(5)=64+17d(5) = 64 + 17
    d(5)=81d(5) = 81

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