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

Substitute n=5: To find the 5th term in the sequence, we need to substitute n=5 into the formula d(n)=(5)/(16)(2)^(n-1).Calculate the exponent: Substitute n=5 into the formula: d(5)=(5)/(16)(2)^(5-1).Calculate 2^4: Calculate the exponent: 2^(5-1) = 2^4.Multiply the result: Calculate 2^4: 2^4 = 2 * 2 * 2 * 2 = 16.Simplify the expression: Multiply the result by (5)/(16): d(5) = (5)/(16) * 16.Expression simplifies to: Simplify the expression: (5)/(16) * 16 = 5 * (16)/(16).Final result: Since (16)/(16) equals 1, the expression simplifies to: 5 * 1 = 5.

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

$d(n)=\frac{5}{16}(2)^{n-1}$ $\newline$ What is the $5^{\text {th }}$ term in the sequence?

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Full solution

d(n)=\frac{5}{16}(2)^{n-1}

\newline

What is the

5^{\text {th }}

term in the sequence?

Substitute $n=5$ : To find the $5^{\text{th}}$ term in the sequence, we need to substitute $n=5$ into the formula $d(n)=\frac{5}{16}(2)^{n-1}$ .
Calculate the exponent: Substitute $n=5$ into the formula: $d(5)=\frac{5}{16}(2)^{5-1}$ .
Calculate $2^4$ : Calculate the exponent: $2^{(5-1)} = 2^4$ .
Multiply the result: Calculate $2^4$ : $2^4 = 2 \times 2 \times 2 \times 2 = 16$ .
Simplify the expression: Multiply the result by $(5)/(16)$ : $d(5) = (5)/(16) \times 16$ .
Expression simplifies to: Simplify the expression: $(\frac{5}{16}) \times 16 = 5 \times (\frac{16}{16})$ .
Final result: Since $(16)/(16)$ equals $1$ , the expression simplifies to: $5 \times 1 = 5$ .