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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