Calculate 3, 6, 12, 24, ..., sum of the first 6 terms

Step by step

The question

Question: 3, 6, 12, 24, …: find the sum of the first 6 terms.

A sequence is a list of numbers in order.

1 Find the ratio

We multiply by 2 every time.

A list like this is a geometric sequence.

The number we multiply by is called the ratio: r = 2.

2 Write S and 2S

S is the sum: all 6 terms added.

Now times 2: each term times 2 is the next term.

So the sum moves one place to the right.

3 Take away

We take S away from 2S.

The terms in the middle are in both rows.

They cross out.

Only 192 and 3 are left.

2S take away S is just S.

192 − 3 is 189.

So the sum of the first 6 terms is 189.

This works for every geometric sequence: the first term, times r to the power n, minus 1, over r minus 1.

4 Check

Let's check: add the 6 terms one by one.

We get 189 again.

So the sum is right!

Let's look back.

First: find the ratio.

Then: write S and 2S.

Then: take away.

Last: check.