# The first term of a geometric sequence is 40, and the common ratio is 0.5. What is the 5th term of the sequence?

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Apr 16, 2018

${T}_{5} = 2.5$

#### Explanation:

The ${n}^{t h}$ term of a geometric progression can be determined by using the formula:

$\textcolor{b l u e}{{T}_{n} = a {r}^{n - 1}}$
where: a = first term and r = common ratio

Substitute the given values of first term and common ratio into the formula:

${T}_{n} = a {r}^{n - 1}$
${T}_{5} = \left(40\right) {\left(0.5\right)}^{5 - 1}$
${T}_{5} = \left(40\right) {\left(0.5\right)}^{4}$
${T}_{5} = \left(40\right) \left(0.0625\right)$
${T}_{5} = 2.5$

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