# The sum of the first #5# terms of a geometric sequence is #93# and the #10#th term is #3/2#. What is the common ratio and what is the fourth term?

##### 1 Answer

If

#### Explanation:

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

#a_n = ar^(n-1)#

where

If

#sum_(n=1)^N a_n = sum_(n=1)^N ar^(n-1) = a(r^N-1)/(r-1)#

In our example, we are given:

#93 = sum_(n=1)^5 a_n = a(r^5-1)/(r-1)#

#ar^9 = a_10 = 3/2#

If this is to have rational solutions, then we should look at the factors of

The prime factorisation of

#93 = 3*31 = 3*(2^5-1)/(2-1)#

So

#3, 6, 12, 24, 48#

But if that were our sequence, then

How about if we reverse the sequence?

#48, 24, 12, 6, 3#

Then the

Is there a typo in the question? Should the

If so, then the common ratio is

If the question is correct in the form given then the answer will be much more messy. Specifically, the common ratio