Sum from i = 1 to 6 of 3i Step by Step

Step by step

The question

Question: work out the sum for i = 1 to 6 of 3i.

Σ_{i = 1}⁶3i

1 Read the sigma

Σ is the Greek letter sigma.

It means: add up.

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

That is 6 − 1 + 1: 6 terms.

For each i we work out 3i.

Σ = add up

start: i = 1, stop: i = 6

6 − 1 + 1 = 6 terms

2 Write the terms

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

We get 3.

i = 1: 3(1) = 3

i = 2 gives 6.

i = 2: 3(2) = 6

i = 3: 3(3) = 9

i = 4: 3(4) = 12

i = 5: 3(5) = 15

And i = 6 gives 18.

That is the last one.

i = 6: 3(6) = 18

3 Add them

Now we add the 6 terms.

Σ_{i = 1}⁶3i = 3 + 6 + 9 + 12 + 15 + 18

So the sum is 63.

= 63

4 Check

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

The terms go up by the same amount, so first plus last, 3 + 18, times 6 terms, over 2.

Pairs: 6 × (3 + 18)2 = 6 × 212 = 63

We get 63 again.

It works!

Let's look back.

First: read the sigma.

Then: write the terms.

Then: add them.

Last: check.

Answer