planhetkk

2022-10-10

The first term in a certain geometric sequence is x and the fourth term in the sequence is 27x, where x is a nonzero number. Which of the following represents the tenth term?

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Johnny Parrish

Expert

The nth term of a geometric sequence is given as:
$a{r}^{n-1}$
Where:
a is the first term, r is the common ratio and n is the nth term.
First term is x
Fourth term is 27x
Using this:
$x{r}^{4-1}=27x$
${r}^{3}=27$
$r=\sqrt[3]{{r}^{3}}=\sqrt[3]{27}=3$
10th term:
${n}_{10}=x{\left(3\right)}^{10-1}=x{\left(3\right)}^{9}$

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