Question

Write a rule for the nth term of the geometric sequence if r = 1/4 and a3 = 2.

Answer 1

Answer:

$a_{n} = 32(\frac{1}{4})^{n-1}$

Step-by-step explanation:

The nth term of a geometric sequence is given by the following equation.

$a_{n+1} = ra_{n}$

In which r is the common ratio.

This can be expanded for the nth term in the following way:

$a_{n} = a_{1}r^{n-1}$

In which $a_{1}$ is the first term.

This means that for example:

$a_{3} = a_{1}r^{3-1}$

So

$a_{3} = a_{1}r^{2}$

$2 = a_{1}(\frac{1}{4})^{2}$

$2 = \frac{a_{1}}{16}$

$a_{1} = 32$

Then

$a_{n} = 32(\frac{1}{4})^{n-1}$