# How do you find nth term rule for #a_1=1/4# and #a_3=6#?

##### 1 Answer

Aug 2, 2016

The formula for the

#a_n = 1/4 (2sqrt(6))^(n-1)#

#a_n = 1/4 (-2sqrt(6))^(n-1)#

#### Explanation:

Assuming this is a geometric sequence...

The general term of a geometric sequence is given by the formula:

#a_n = ar^(n-1)#

where

So we have

#r^2 = (ar^2)/(ar^0) = a_3/a_1 = 6/(1/4) = 24#

So:

#r = +-sqrt(24) = +-2sqrt(6)#

So the formula for the

#a_n = 1/4 (2sqrt(6))^(n-1)#

#a_n = 1/4 (-2sqrt(6))^(n-1)#