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{[d(1)=(1)/(12)],[d(n)=d(n-1)*(-6)]:} What is the 4^("th ") term in the sequence?

{d(1)=112d(n)=d(n−1)⋅(−6) \left\{\begin{array}{l} d(1)=\frac{1}{12} \\ d(n)=d(n-1) \cdot(-6) \end{array}\right. \newlineWhat is the 4th  4^{\text {th }} term in the sequence?

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Full solution

Q. {d(1)=112d(n)=d(n−1)⋅(−6) \left\{\begin{array}{l} d(1)=\frac{1}{12} \\ d(n)=d(n-1) \cdot(-6) \end{array}\right. \newlineWhat is the 4th  4^{\text {th }} term in the sequence?
  1. Identify First Term: Identify the first term of the sequence.\newlineThe first term d(1)d(1) is given as 112\frac{1}{12}.
  2. Find Second Term: Use the recursive formula to find the second term.\newlineThe recursive formula is d(n)=d(n−1)×(−6)d(n) = d(n-1) \times (-6). To find the second term, we use the first term:\newlined(2)=d(1)×(−6)=(112)×(−6)=−12d(2) = d(1) \times (-6) = \left(\frac{1}{12}\right) \times (-6) = -\frac{1}{2}.
  3. Find Third Term: Use the recursive formula to find the third term.\newlineNow we use the second term to find the third term:\newlined(3)=d(2)×(−6)=(−12)×(−6)=3d(3) = d(2) \times (-6) = \left(-\frac{1}{2}\right) \times (-6) = 3.
  4. Find Fourth Term: Use the recursive formula to find the fourth term.\newlineUsing the third term to find the fourth term:\newlined(4)=d(3)⋅(−6)=3⋅(−6)=−18d(4) = d(3) \cdot (-6) = 3 \cdot (-6) = -18.

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