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b(n)=-1(2)^(n-1) What is the 5^("th ") term in the sequence?

b(n)=−1(2)n−1 b(n)=-1(2)^{n-1} \newlineWhat is the 5th  5^{\text {th }} term in the sequence?

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Full solution

Q. b(n)=−1(2)n−1 b(n)=-1(2)^{n-1} \newlineWhat is the 5th  5^{\text {th }} term in the sequence?
  1. Sequence definition: Understand the sequence definition.\newlineThe sequence is defined by the formula b(n)=−1(2)(n−1)b(n) = -1(2)^{(n-1)}, which means that to find the nnth term, we need to substitute the value of nn into the formula and simplify.
  2. Substitute nn with 55: Substitute nn with 55 to find the 55th term.\newlineWe need to find b(5)b(5), so we substitute nn with 55 in the formula: b(5)=−1(2)5−1b(5) = -1(2)^{5-1}.
  3. Simplify the exponent: Simplify the exponent.\newlineCalculate 2(5−1)2^{(5-1)} which is 242^4.\newline24=2×2×2×2=162^4 = 2 \times 2 \times 2 \times 2 = 16.
  4. Apply the −1 -1 coefficient: Apply the −1 -1 coefficient.\newlineNow, multiply the result from Step 33 by −1 -1 : b(5)=−1×16 b(5) = -1 \times 16 .
  5. Calculate the 55th term: Calculate the 55th term. b(5)=−1×16=−16b(5) = -1 \times 16 = -16.

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