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

b(n)=1(−2)n−1 b(n)=1(-2)^{n-1} \newlineWhat is the 4th  4^{\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 4th  4^{\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 value of n=44: Substitute the value of n=44 into the formula to find the 44th term.\newlineWe have b(44)=11(−2-2)^{(44−1-1)}.
  3. Simplify the exponent: Simplify the exponent.\newlineCalculate (−2)(4−1)(-2)^{(4-1)} which is (−2)3(-2)^3.
  4. Calculate (−2)3(-2)^3: Calculate the value of (−2)3(-2)^3.\newline(−2)3(-2)^3 is −2×−2×−2-2 \times -2 \times -2, which equals −8-8.
  5. Multiply by 11: Multiply the result by 11 as per the sequence definition.\newline1×−81 \times -8 equals −8-8.

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