Sum from i = 1 to 3 of 5i Step by Step

Step by step

The question

Question: work out the sum for i = 1 to 3 of 5i.

Σ_{i = 1}³5i

1 Read the sigma

Σ is the Greek letter sigma.

It means: add up.

Start with i = 1, and stop at i = 3.

That is 3 − 1 + 1: 3 terms.

For each i we work out 5i.

Σ = add up

start: i = 1, stop: i = 3

3 − 1 + 1 = 3 terms

2 Write the terms

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

We get 5.

i = 1: 5(1) = 5

i = 2 gives 10.

i = 2: 5(2) = 10

And i = 3 gives 15.

That is the last one.

i = 3: 5(3) = 15

3 Add them

Now we add the 3 terms.

Σ_{i = 1}³5i = 5 + 10 + 15

So the sum is 30.

= 30

4 Check

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

The terms go up by the same amount, so first plus last, 5 + 15, times 3 terms, over 2.

Pairs: 3 × (5 + 15)2 = 3 × 202 = 30

We get 30 again.

It works!

Let's look back.

First: read the sigma.

Then: write the terms.

Then: add them.

Last: check.

Answer