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{[a(1)=-13],[a(n)=a(n-1)+4]:} Find the 2^("nd ") term in the sequence.

{a(1)=−13a(n)=a(n−1)+4 \left\{\begin{array}{l} a(1)=-13 \\ a(n)=a(n-1)+4 \end{array}\right. \newlineFind the 2nd  2^{\text {nd }} term in the sequence.

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Full solution

Q. {a(1)=−13a(n)=a(n−1)+4 \left\{\begin{array}{l} a(1)=-13 \\ a(n)=a(n-1)+4 \end{array}\right. \newlineFind the 2nd  2^{\text {nd }} term in the sequence.
  1. Identify first term and common difference: Identify the first term of the sequence and the common difference.\newlineThe first term a(1)a(1) is given as −13-13. The common difference is the amount added to each term to get the next term, which is given as 44.
  2. Calculate second term using common difference: Calculate the second term using the common difference.\newlineThe second term a(2)a(2) is found by adding the common difference to the first term: a(2)=a(1)+4a(2) = a(1) + 4.\newlinea(2)=−13+4=−9a(2) = -13 + 4 = -9.

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