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{[c(1)=(3)/(16)],[c(n)=c(n-1)*4]:} What is the 3^("rd ") term in the sequence?

{c(1)=316c(n)=c(n−1)⋅4 \left\{\begin{array}{l} c(1)=\frac{3}{16} \\ c(n)=c(n-1) \cdot 4 \end{array}\right. \newlineWhat is the 3rd  3^{\text {rd }} term in the sequence?

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Full solution

Q. {c(1)=316c(n)=c(n−1)⋅4 \left\{\begin{array}{l} c(1)=\frac{3}{16} \\ c(n)=c(n-1) \cdot 4 \end{array}\right. \newlineWhat is the 3rd  3^{\text {rd }} term in the sequence?
  1. Identify Given Sequence: Identify the given sequence and the formula for the nnth term.\newlineThe sequence is defined by the recursive formula c(n)=c(n−1)×4c(n) = c(n-1) \times 4, with the first term c(1)=316c(1) = \frac{3}{16}.
  2. Find Second Term: Find the second term using the recursive formula.\newlineTo find the second term, we use the first term and multiply it by 44.\newlinec(2)=c(1)×4=(316)×4c(2) = c(1) \times 4 = \left(\frac{3}{16}\right) \times 4
  3. Calculate Second Term: Calculate the second term.\newlinec(2)=316×4=34c(2) = \frac{3}{16} \times 4 = \frac{3}{4}
  4. Find Third Term: Find the third term using the recursive formula.\newlineNow, we use the second term to find the third term.\newlinec(3)=c(2)×4=(34)×4c(3) = c(2) \times 4 = \left(\frac{3}{4}\right) \times 4
  5. Calculate Third Term: Calculate the third term. c(3)=(34)×4=3c(3) = \left(\frac{3}{4}\right) \times 4 = 3

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