Question

What is the tenth term?

Answer 1

Answer:

$\large\boxed{\dfrac{1}{243}}$

Step-by-step explanation:

It's a geometric sequence:

$a_1=81\\\\a_2=a_1\cdot\dfrac{1}{3}\to a_2=81\cdot\dfrac{1}{3}=27\\\\a_3=a_2\cdot\dfrac{1}{3}\to a_3=27\cdot\dfrac{1}{3}=9\\\vdots$

The explicit formula of a geometric sequence:

$a_n=a_1r^{n-1}$

Substitute:

$a_1=81,\ r=\dfrac{1}{3}\\\\a_n=81\left(\dfrac{1}{3}\right)^{n-1}$

Calculate the 10th term. Substitute n = 10:

$a_{10}=81\left(\dfrac{1}{3}\right)^{10-1}=3^4\left(\dfrac{1}{3}\right)^9=3^4\cdot\dfrac{1}{3^9}=\dfrac{3^4}{3^9}=\dfrac{1}{3^5}=\dfrac{1}{243}$