Question

What is the value of the fourth term in a geometric sequence for which `a_1` = 15 and r = 1/3?

Answer 1

`a_4=5/9`

Explanation:

The standard geometric sequence is.

`color(red)(|bar(ul(color(white)(a/a)color(black)(a,ar,ar^2,ar^3,......)color(white)(a/a)|)))`
where the first term is represented by a, and each term of the sequence is obtained by multiplying the previous term by r, the common ratio.
The nth term is `color(red)(|bar(ul(color(white)(a/a)color(black)(a_n=ar^(n-1))color(white)(a/a)|)))`

Here a = `a_1=15" and " r=1/3`

`rArra_4=15xx(1/3)^3=15xx1/27=5/9`