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{[a(1)=20],[a(n)=a(n-1)-17]:} Find the 3^("rd ") term in the sequence.

{a(1)=20a(n)=a(n−1)−17 \left\{\begin{array}{l} a(1)=20 \\ a(n)=a(n-1)-17 \end{array}\right. \newlineFind the 3rd  3^{\text {rd }} term in the sequence.

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Full solution

Q. {a(1)=20a(n)=a(n−1)−17 \left\{\begin{array}{l} a(1)=20 \\ a(n)=a(n-1)-17 \end{array}\right. \newlineFind the 3rd  3^{\text {rd }} term in the sequence.
  1. Identify First Term: Identify the first term in the sequence.\newlineThe first term a(1)a(1) is given as 2020.
  2. Find Second Term: Use the recursive formula to find the second term. The recursive formula is a(n)=a(n−1)−17a(n) = a(n-1) - 17. To find the second term, a(2)a(2), we use the first term a(1)=20a(1) = 20. a(2)=a(1)−17=20−17=3a(2) = a(1) - 17 = 20 - 17 = 3.
  3. Find Third Term: Use the recursive formula to find the third term.\newlineNow we use the second term to find the third term using the same recursive formula.\newlinea(3)=a(2)−17=3−17=−14a(3) = a(2) - 17 = 3 - 17 = -14.

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