Find the sum of the geometric sequence. 1, 1/4, 1/16, 1/64, 1/256

A geometric sequence is characterized by a common ratio.

The sum of the geometric terms is:

The sequence is given as:

First, we calculate the common ratio

This is calculated by dividing the second term by the first term

The sum of terms of a geometric sequence is:

Where

n = 5 --- the number of terms

a = 1 -- the first term

So, we have:

Subtract

Express as products

Hence, the sum of the geometric terms is:

Read more about geometric sequence at:

link

in a geometric sequence, we get the next term by multiplying the current term by the "common ratio".

now, if we simply divide the any of the terms by the one before it, their quotient is, yeap, you guessed it, is the "common ratio".

anyhow, divide say (1/16) ÷ (1/4) or (1/256) ÷ (1/64), and you'll find it's 1/4.

bearing in mind that there are 5 terms, and the first one is 1.