d(n)=-5((1)/(2))^(n-1) What is the 3^("rd ") term in the sequence?

Understanding the sequence formula: Understand the given sequence formula. The sequence is defined by the formula d(n)=-5((1)/(2))^(n-1), which suggests that it is a geometric sequence with a common ratio of (1/2) and a starting term multiplied by -5.Finding the 3rd term: Plug in the value of n to find the 3rd term. To find the 3rd term, we substitute n=3 into the formula. d(3) = -5((1)/(2))^(3-1)Calculating the exponent: Calculate the exponent part of the formula. (1/2)^(3-1) = (1/2)^2Simplifying the exponent: Simplify the exponent. (1/2)^2 = 1/4Multiplying by -5 to get the 3rd term: Multiply the result of the exponent by -5 to get the 3rd term. d(3) = -5 * (1/4)Performing the multiplication: Perform the multiplication to find the 3rd term. d(3) = -5/4

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

$d(n)=-5\left(\frac{1}{2}\right)^{n-1}$ $\newline$ What is the $3^{\text {rd }}$ term in the sequence?

View step-by-step help

Full solution

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

\newline

What is the

3^{\text {rd }}

term in the sequence?

Understanding the sequence formula: Understand the given sequence formula. $\newline$ The sequence is defined by the formula $d(n)=-5\left(\frac{1}{2}\right)^{n-1}$ , which suggests that it is a geometric sequence with a common ratio of $\frac{1}{2}$ and a starting term multiplied by $-5$ .
Finding the $3$ rd term: Plug in the value of $n$ to find the $3$ rd term. $\newline$ To find the $3$ rd term, we substitute $n=3$ into the formula. $\newline$ $d(3) = -5\left(\frac{1}{2}\right)^{3-1}$
Calculating the exponent: Calculate the exponent part of the formula. $(\frac{1}{2})^{(3-1)} = (\frac{1}{2})^2$
Simplifying the exponent: Simplify the exponent. $\newline$ $(\frac{1}{2})^2 = \frac{1}{4}$
Multiplying by $-5$ to get the $3$ rd term: Multiply the result of the exponent by $-5$ to get the $3$ rd term. $\newline$ $d(3) = -5 \times \left(\frac{1}{4}\right)$
Performing the multiplication: Perform the multiplication to find the $3^{\text{rd}}$ term. $d(3) = -\frac{5}{4}$