Question

Find the 9th term of the geometric sequence whose common ratio is 1/3 and whose first term is 2.

Answer 1

2/6561

Explanation:

Geometric sequence formula :
`a_n=a_1(r)^n^-^1`

where an = nth term, a1 = first term , r = common ratio and n = term position

given ratio : 1/3 , first term : 2 , given this we want to find the 9th term

to do so we simply plug in what we are given into the formula

recall formula :
`a_n=a_1(r)^n^-^1`

define variables : a1 = 2 , r = 1/3 , n = 9

plug in values

a9 = 2(1/3)^(9-1)

subtract exponents

a9 = 2(1/3)^8

evaluate exponent

a9 = 2 (1/6561)

multiply 2 and 1/6561

a9 = 2/6561