Question

Someone please explain step by step.

Find the 10th term of the geometric sequence whose common ratio is 1/2
and whose first term is 5.
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Answer 1

Answer:

${10}^{th} \: term = \frac{5}{512}$

Step-by-step explanation:

geometric progression formula:

${n}^{th} \: term = ar ^{n - 1}$

given:

common ratio, r = 1/2

$first \: term \: = 5$

1) find the value of a

${n}^{th} \: term \: = a {r}^{n - 1}$

we're finding the 1st term, so substitute 1 into n:

${1}^{st} \: term = a( \frac{1}{2} ) {}^{1 - 1}$

first term is 5. so we substitute 5 into the equation:

$5 = a(1)$

$a = 5$

2) find the 10th term

we're finding the 10th term, so substitute 10 into the equation and don't forget to substitute 5 into a:

${10}^{th} \: term = 5( \frac{1}{2} ) {}^{10 - 1}$

${10}^{th} \: term = 5( \frac{1}{512} )$

${10}^{th} \: term = \frac{5}{512}$