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d(n)=3(-2)^(n-1) What is the 4^("th ") term in the sequence?

d(n)=3(−2)n−1 d(n)=3(-2)^{n-1} \newlineWhat is the 4th  4^{\text {th }} term in the sequence?

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Full solution

Q. d(n)=3(−2)n−1 d(n)=3(-2)^{n-1} \newlineWhat is the 4th  4^{\text {th }} term in the sequence?
  1. Understand formula: Understand the given sequence formula.\newlineThe formula d(n)=3(−2)(n−1)d(n)=3(-2)^{(n-1)} defines a sequence where each term is generated by plugging in the position number nn into the formula.
  2. Find 44th term: Plug in the value of n=4n=4 to find the 44th term.\newlineWe need to find d(4)d(4), which means we will substitute nn with 44 in the formula.\newlined(4)=3(−2)4−1d(4)=3(-2)^{4-1}
  3. Simplify exponent: Simplify the exponent.\newlineCalculate the value of (−2)(4−1)(-2)^{(4-1)}, which is (−2)3(-2)^3.\newline(−2)3=−2×−2×−2=−8(-2)^3 = -2 \times -2 \times -2 = -8
  4. Multiply by 33: Multiply the result by 33. Now, multiply the result from Step 33 by 33 as per the sequence formula. d(4)=3×(−8)=−24d(4) = 3 \times (-8) = -24

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