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

Sequence definition: Understand the sequence definition. The sequence is defined by the formula b(n) = -1(2)^(n-1), which means that to find the nth term, we need to substitute the value of n into the formula and simplify.Substitute n with 5: Substitute n with 5 to find the 5th term. We need to find b(5), so we substitute n with 5 in the formula: b(5) = -1(2)^(5-1).Simplify the exponent: Simplify the exponent. Calculate 2^(5-1) which is 2^4. 2^4 = 2 * 2 * 2 * 2 = 16.Apply the -1 coefficient: Apply the -1 coefficient. Now, multiply the result from Step 3 by -1: b(5) = -1 * 16.Calculate the 5th term: Calculate the 5th term. b(5) = -1 * 16 = -16.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

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

View step-by-step help

Full solution

b(n)=-1(2)^{n-1}

\newline

What is the

5^{\text {th }}

term in the sequence?

Sequence definition: Understand the sequence definition. $\newline$ The sequence is defined by the formula $b(n) = -1(2)^{(n-1)}$ , which means that to find the $n$ th term, we need to substitute the value of $n$ into the formula and simplify.
Substitute $n$ with $5$ : Substitute $n$ with $5$ to find the $5$ th term. $\newline$ We need to find $b(5)$ , so we substitute $n$ with $5$ in the formula: $b(5) = -1(2)^{5-1}$ .
Simplify the exponent: Simplify the exponent. $\newline$ Calculate $2^{(5-1)}$ which is $2^4$ . $\newline$ $2^4 = 2 \times 2 \times 2 \times 2 = 16$ .
Apply the $-1$ coefficient: Apply the $-1$ coefficient. $\newline$ Now, multiply the result from Step $3$ by $-1$ : $b(5) = -1 \times 16$ .
Calculate the $5$ th term: Calculate the $5$ th term. $b(5) = -1 \times 16 = -16$ .