Write 3 + 6 + 9 + 12 + 15 using sigma notation

Step by step

The question

Question: write 3 + 6 + 9 + 12 + 15 using sigma notation.

1 Find the rule

The rule from the sequences lesson, with i for the term number: the first term, plus (i − 1) times 3.

Open the bracket: i times 3 is 3i, and −1 times 3 is −3.

Plain numbers go together.

So the rule is 3i.

2 Count the terms

i counts the terms: 1, 2, 3, 4, 5.

There are 5 terms.

So i starts at 1 and stops at 5.

Careful!

The stop number on Σ is the last i, 5.

It is not the last term, 15.

3 Write it with Σ

So we write: the sum for i = 1 to 5 of 3i.

4 Check

Let's check: put i = 1, 2, up to 5 into 3i.

i = 1 gives 3, i = 2 gives 6, and so on.

That is the sum we started with.

It works!

Let's look back.

First: find the rule.

Then: count the terms.

Then: write it with Σ.

Last: check.