Question

3, 1, 1/3

Find the 7th term.

Answer 1

a7 = 1/243

Explanation:

The formula for the nth term of a geometric series is

`a_(n)=a_(1)r^n^-^1`, where a1 is the first term, r is the common ratio, and n is the position of the term (e.g., 6th or 3rd).

First, we need to find the common ratio.

We can find it by dividing the second term (1) by the first term (3):

`r=(a_(2) )/(a_(1) )=(1)/(3)`

Since we already know a1 and r, we simply substitute 7 for n to find the 7th term:

`a_(7)=3*(1)/(3) ^7^-^1\\a_(7)=3*(1)/(3)^6\\ a_(7)=3*(1)/(729)\\ a_(7)=(1)/(243)`