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{[c(1)=6],[c(n)=c(n-1)-16]:} Find the 3^("rd ") term in the sequence.

{c(1)=6c(n)=c(n−1)−16 \left\{\begin{array}{l} c(1)=6 \\ c(n)=c(n-1)-16 \end{array}\right. \newlineFind the 3rd  3^{\text {rd }} term in the sequence.

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Full solution

Q. {c(1)=6c(n)=c(n−1)−16 \left\{\begin{array}{l} c(1)=6 \\ c(n)=c(n-1)-16 \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, c(1)c(1), is given as 66.
  2. Determine Common Difference: Determine the common difference in the sequence.\newlineThe sequence is defined by c(n)=c(n−1)−16c(n) = c(n-1) - 16, which means the common difference is −16-16.
  3. Calculate Second Term: Calculate the second term in the sequence using the common difference.\newlineThe second term, c(2)c(2), is c(1)−16c(1) - 16.\newlinec(2)=6−16=−10c(2) = 6 - 16 = -10.
  4. Calculate Third Term: Calculate the third term in the sequence using the common difference.\newlineThe third term, c(3)c(3), is c(2)−16c(2) - 16.\newlinec(3)=−10−16=−26c(3) = -10 - 16 = -26.

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