Sum from i = 1 to 4 of 3 × 2^(i-1) Step by Step

Step by step

The question

Question: work out the sum for i = 1 to 4 of 3 × 2 to the power (i − 1).

Σ_{i = 1}⁴3 × 2^{i − 1}

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 3 × 2 to the power (i − 1).

Σ = add up

start: i = 1, stop: i = 4

4 − 1 + 1 = 4 terms

2 Write the terms

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

We get 3.

i = 1: 3 × 2⁰ = 3

i = 2 gives 6.

i = 2: 3 × 2¹ = 6

i = 3: 3 × 2² = 12

And i = 4 gives 24.

That is the last one.

i = 4: 3 × 2³ = 24

3 Add them

Now we add the 4 terms.

Σ_{i = 1}⁴3 × 2^{i − 1} = 3 + 6 + 12 + 24

So the sum is 45.

= 45

4 Check

Let's check: we add them again, backwards.

Backwards: 24 + 12 + 6 + 3 = 45

We get 45 again.

It works!

Let's look back.

First: read the sigma.

Then: write the terms.

Then: add them.

Last: check.

Answer