Solve a_n = 3a_(n-1), a_0 = 4

Step by step

The question

Question: solve aₙ = 3aₙ₋₁, starting with a₀ = 4.

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 a₀ = 4.

Then 3 times 4.

That is 12.

And so on.

2 Times 3 each time

The rule only multiplies by 3 each time.

Careful!

Times 3 again and again is a power of 3, not adding.

3 The formula

So aₙ is 4 times 3 to the n.

4 Check

Check n = 3 with the formula: it gives 108.

The table says 108 too.

Right!

Let's look back.

First: first terms.

Then: times 3 each time.

Then: the formula.

Last: check.