How do you find a formula for the nth term of the geometric sequence: 500, 100, 20, 4, ...?

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How do you find a formula for the nth term of the geometric sequence: 500, 100, 20, 4, ...?

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Answer 1 · 2016-04-29T00:39:20

$t_{n} = a {(\frac{1}{5})}^{n - 1}$ $t_n=a(1/5)^(n-1)$

Explanation:

Recall that the formula for the $n^{th}$ $n^("th")$ of a geometric sequence is:

$color(blue)(|bar(ul(color(white)(a/a)t_n=ar^(n-1)color(white)(a/a)|)))$

where:
$t_n=$ term number
$a=$ first term
$r=$ common ratio
$n=$ number of terms

Start by determining the value of $a$ , the first term of the sequence. In your case, that would be $500$ .

Use $a=500$ , and $t_2=100$ to create an equation representing the second term.

$t_n=ar^(n-1)$

$100=500r^(2-1)$

Solve for $r$ .

$r=1/5$

Now that you have the value of $r$ , you can make a formula representing the $n^("th")$ term of the geometric sequence.

$color(green)(|bar(ul(color(white)(a/a)t_n=a(1/5)^(n-1)color(white)(a/a)|)))$

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How do you find a formula for the nth term of the geometric sequence: 500, 100, 20, 4, ...?

1 Answer

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