Solve a_n = 5a_(n-1), a_0 = 2

Step by step

The question

Question: solve aₙ = 5aₙ₋₁, starting with a₀ = 2.

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 = 2.

Then 5 times 2.

That is 10.

And so on.

2 Times 5 each time

The rule only multiplies by 5 each time.

Careful!

Times 5 again and again is a power of 5, not adding.

3 The formula

So aₙ is 2 times 5 to the n.

4 Check

Check n = 3 with the formula: it gives 250.

The table says 250 too.

Right!

Let's look back.

First: first terms.

Then: times 5 each time.

Then: the formula.

Last: check.