Sum from i = 1 to 4 of (i + 3)

Step by step

The question

Question: work out the sum for i = 1 to 4 of (i + 3).

1 Read the sigma

Σ is the Greek letter sigma.

It means: add up.

Start with i = 1, and stop at i = 4.

That is 4 − 1 + 1: 4 terms.

For each i we work out i + 3.

Careful!

The + 3 is inside the bracket.

So it is added in every term, 4 times, not just once.

2 Write the terms

i = 1: we put 1 in place of i.

We get 4.

i = 2 gives 5.

And i = 4 gives 7.

That is the last one.

3 Add them

Now we add the 4 terms.

So the sum is 22.

4 Check

Let's check with the pairs from the sequences lesson.

The terms go up by the same amount, so first plus last, 4 + 7, times 4 terms, over 2.

We get 22 again.

It works!

Let's look back.

First: read the sigma.

Then: write the terms.

Then: add them.

Last: check.