# How do you find the fifth term in a geometric sequence in which the fourth term is 5, the sixth term is 7, and the common ratio is negative?

##### 2 Answers

Nov 29, 2015

#### Answer:

#### Explanation:

**5th term**

hope that helped

Nov 29, 2015

#### Answer:

The fifth term will be a geometric mean of the fourth and sixth term.

Since the common ratio is negative it will be

#### Explanation:

The general form of a term of a geometric sequence is:

#a^n = a r^(n-1)#

Where

We are given

So

So

Then

Or just taking the geometric mean of

#a_5 = +-sqrt(a_4 * a_6) = +-sqrt(35)#

and we need to use the negative square root to get a negative common ratio.