Question

What is the tenth term?

Answer 1

`\large\boxed{(1)/(243)}`

Explanation:

It's a geometric sequence:

`a_1=81\\\\a_2=a_1\cdot(1)/(3)\to a_2=81\cdot(1)/(3)=27\\\\a_3=a_2\cdot(1)/(3)\to a_3=27\cdot(1)/(3)=9\\\vdots`

The explicit formula of a geometric sequence:

`a_n=a_1r^(n-1)`

Substitute:

`a_1=81,\ r=(1)/(3)\\\\a_n=81\left((1)/(3)\right)^(n-1)`

Calculate the 10th term. Substitute n = 10:

`a_(10)=81\left((1)/(3)\right)^(10-1)=3^4\left((1)/(3)\right)^9=3^4\cdot(1)/(3^9)=(3^4)/(3^9)=(1)/(3^5)=(1)/(243)`