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

1 Answer
Johnson Z.
Apr 29, 2016

t_n=a(1/5)^(n-1)

Explanation:

Recall that the formula for the 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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