# What is the fifth term of the following sequence? $$a_n = \left(-\dfrac{1}{2}\right)^{n - 1}$$

## Question:

What is the fifth term of the following sequence?

$$a_n = \left(-\dfrac{1}{2}\right)^{n - 1}$$

## Sequence:

A sequence is comprised of a finite or infinite number of terms (or items) arranged in a certain order. For example, the {eq}n{/eq}th term of the sequence {eq}3, 5, 7, 9, \dots {/eq} can be expressed as:

$${a_n} = 2n + 1$$

where {eq}n {/eq} indicates the term number.

If we know the {eq}n{/eq}th term of a sequence, we can easily determine the value of a specific term by directly substituting the term number.

## Answer and Explanation:

The {eq}n{/eq}th term of the given sequence is

$${a_n} = {\left( { - \dfrac{1}{2}} \right)^{n - 1}}$$

Substitute {eq}n=5 {/eq} in the given expression to evaluate the fifth term of the sequence.

\begin{align*} {a_5} &= {\left( { - \dfrac{1}{2}} \right)^{5 - 1}}\\[0.3cm] &= {\left( { - \dfrac{1}{2}} \right)^4}\\[0.3cm] &= \dfrac{1}{{{{\left( 2 \right)}^4}}}&\left[ \ {{\rm{Use}}\;{\rm{the \ formula}}\;{{\left( { - 1} \right)}^n} = 1\;{\rm{if}}\;n\;{\rm{is}}\;{\rm{even}}} \ \right]\\[0.3cm] &= \dfrac{1}{{16}} \end{align*}\\

Thus, the fifth term of the sequence is {eq}\bf{\dfrac{1}{{16}}} {/eq}.