# How do you find the missing terms of the geometric sequence:2, __, __, __, 512, ...?

##### 2 Answers

There are four possibilities:

#8, 32, 128#

#-8, 32, -128#

#8i, -32, -128i#

#-8i, -32, 128i#

#### Explanation:

We are given:

#{ (a_1 = 2), (a_5 = 512) :}#

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

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

where

So we find:

#r^4 = (ar^4)/(ar^0) = a_5/a_1 = 512/2 = 256 = 4^4#

The possible values for

#+-4# ,#+-4i#

For each of these possible common ratios, we can fill in

#8, 32, 128#

#-8, 32, -128#

#8i, -32, -128i#

#-8i, -32, 128i#

The **Missing Terms** are,

#### Explanation:

Let

Then,

But, we know that,

Hence, the reqd. missing terms, known as, **Intermediate**

**Geometric Means,** are,

**Enjoy Maths.!**