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d(n)=(5)/(16)(2)^(n-1) What is the 5^("th ") term in the sequence?

d(n)=516(2)n−1 d(n)=\frac{5}{16}(2)^{n-1} \newlineWhat is the 5th  5^{\text {th }} term in the sequence?

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Full solution

Q. d(n)=516(2)n−1 d(n)=\frac{5}{16}(2)^{n-1} \newlineWhat is the 5th  5^{\text {th }} term in the sequence?
  1. Substitute n=5n=5: To find the 5th5^{\text{th}} term in the sequence, we need to substitute n=5n=5 into the formula d(n)=516(2)n−1d(n)=\frac{5}{16}(2)^{n-1}.
  2. Calculate the exponent: Substitute n=5n=5 into the formula: d(5)=516(2)5−1d(5)=\frac{5}{16}(2)^{5-1}.
  3. Calculate 242^4: Calculate the exponent: 2(5−1)=242^{(5-1)} = 2^4.
  4. Multiply the result: Calculate 242^4: 24=2×2×2×2=162^4 = 2 \times 2 \times 2 \times 2 = 16.
  5. Simplify the expression: Multiply the result by (5)/(16)(5)/(16): d(5)=(5)/(16)×16d(5) = (5)/(16) \times 16.
  6. Expression simplifies to: Simplify the expression: (516)×16=5×(1616)(\frac{5}{16}) \times 16 = 5 \times (\frac{16}{16}).
  7. Final result: Since (16)/(16)(16)/(16) equals 11, the expression simplifies to: 5×1=55 \times 1 = 5.

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