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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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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Answer 1 · 2018-04-16T07:28:45

$T_{5} = 2.5$ $T_5 = 2.5$

Explanation:

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

$T_{n} = a r^{n - 1}$ $color(blue)(T_n = ar^(n-1))$
where: a = first term and r = common ratio

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

$T_{n} = a r^{n - 1}$ $T_n = ar^(n-1)$
$T_{5} = (40) {(0.5)}^{5 - 1}$ $T_5 = (40)(0.5)^(5-1)$
$T_{5} = (40) {(0.5)}^{4}$ $T_5 = (40)(0.5)^(4)$
$T_{5} = (40) (0.0625)$ $T_5 = (40)(0.0625)$
$T_{5} = 2.5$ $T_5 = 2.5$

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

1 Answer

Explanation:

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