# How do you find the number of terms in the following geometric series: 1 + 2 + 4 + ... + 67108864?

##### 2 Answers

Identify the appropriate power of

#### Explanation:

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

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

where

In our example,

Notice that

#2^26 = 2^6 * 2^10 * 2^10 = 64*1024*1024#

So there are

**Footnote**

As a child, I used to like to write powers of

In later life I found it useful to memorise powers of

A couple of 'fun' ones are

#### Explanation:

It was calculated that the

where

In the given question,

(To take it further from where @George C. left in his solution)

To find

or