Sum from n = 1 to 6 of (n + 10)

Step by step

The question

Question: work out the sum for n = 1 to 6 of (n + 10).

1 Read the sigma

Σ is the Greek letter sigma.

It means: add up.

Start with n = 1, and stop at n = 6.

That is 6 − 1 + 1: 6 terms.

For each n we work out n + 10.

Careful!

The + 10 is inside the bracket.

So it is added in every term, 6 times, not just once.

2 Write the terms

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

We get 11.

n = 2 gives 12.

And n = 6 gives 16.

That is the last one.

3 Add them

Now we add the 6 terms.

So the sum is 81.

4 Check

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

The terms go up by the same amount, so first plus last, 11 + 16, times 6 terms, over 2.

We get 81 again.

It works!

Let's look back.

First: read the sigma.

Then: write the terms.

Then: add them.

Last: check.