Write 10 + 7 + 4 + 1 - 2 using sigma notation

Step by step

The question

Question: write 10 + 7 + 4 + 1 − 2 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 + 13.

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, −2.

3 Write it with Σ

So we write: the sum for i = 1 to 5 of −3i + 13.

4 Check

Let's check: put i = 1, 2, up to 5 into −3i + 13.

i = 1 gives 10, i = 2 gives 7, 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.