How do you write a rule for the nth term of the geometric sequence given the two terms #a_2=36, a_4=576#?

1 Answer
May 16, 2017

Answer:

See explanation.

Explanation:

For any geometric sequence #a_n#, and natural #n,k# #(n>k)# you can write that:

#a_n=a_k*q^(n-k)#

In this task we can write that:

#576=36q^2#

#q^2=16#

This leads to 2 possible values of #q#: #q_1=-4# and #q_2=4#

Now we can calculate the first term separately for #q=-4# and #q=4#

If #q=-4# then #a_1=36/(-4)=-9#

else if #q=4# then #a_1=36/4=9#

So this task has 2 solutions:

#a_n=(-9)*(-4)^(n-1)# or #a_n=9*4^(n-1)#