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{[d(1)=13],[d(n)=d(n-1)+17]:} Find the 4^("th ") term in the sequence.

{d(1)=13d(n)=d(n−1)+17 \left\{\begin{array}{l} d(1)=13 \\ d(n)=d(n-1)+17 \end{array}\right. \newlineFind the 4th  4^{\text {th }} term in the sequence.

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Full solution

Q. {d(1)=13d(n)=d(n−1)+17 \left\{\begin{array}{l} d(1)=13 \\ d(n)=d(n-1)+17 \end{array}\right. \newlineFind the 4th  4^{\text {th }} term in the sequence.
  1. Given information: We are given the first term of the sequence, d(1)=13d(1) = 13, and the recursive formula for the sequence, d(n)=d(n−1)+17d(n) = d(n-1) + 17. To find the 4th4^{\text{th}} term, we need to apply the recursive formula three times starting from the first term.
  2. Find second term: First, we find the second term using the recursive formula: d(2)=d(1)+17=13+17=30d(2) = d(1) + 17 = 13 + 17 = 30.
  3. Find third term: Next, we find the third term using the recursive formula: d(3)=d(2)+17=30+17=47d(3) = d(2) + 17 = 30 + 17 = 47.
  4. Find fourth term: Finally, we find the fourth term using the recursive formula: d(4)=d(3)+17=47+17=64d(4) = d(3) + 17 = 47 + 17 = 64.

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