Solve a_n = 2a_(n-1), a_1 = 3

Step by step

The question

Question: solve aₙ = 2aₙ₋₁, starting with a₁ = 3.

Solve means: find a formula for aₙ, so we can get any term without the ones before.

1 First terms

First, a few terms.

Each one comes from the one before.

We start with a₁ = 3.

Then 2 times 3.

That is 6.

And so on.

2 Times 2 each time

The rule only multiplies by 2 each time.

Careful!

Times 2 again and again is a power of 2, not adding.

3 The formula

So aₙ is 3 times 2 to the n − 1.

4 Check

Check n = 4 with the formula: it gives 24.

The table says 24 too.

Right!

Let's look back.

First: first terms.

Then: times 2 each time.

Then: the formula.

Last: check.