Step by step
The question
Question: solve aₙ = aₙ₋₁ − 3, starting with a₀ = 20.
an = an − 1 − 3, a0 = 20
Solve means: find a formula for aₙ, so we can get any term without the ones before.
solve = a formula for an
1 First terms
First, a few terms.
Each one comes from the one before.
We start with a₀ = 20.
start
20
Then 20, minus 3.
20 − 3
That is 17.
And so on.
17
17 − 3
14
14 − 3
11
11 − 3
8
2 Take away 3 each time
The rule only takes away 3 each time.
After n steps from the start we have taken away 3 that many times.
take away 3 each time
Careful!
From a 0 to a n there are n steps.
Careful: n steps from a₀ to aₙ
3 The formula
So aₙ = 20 − 3n.
an = 20 − 3n
4 Check
Check n = 3 with the formula: it gives 11.
n = 3: formula gives 11
The table says 11 too.
Right!
table: a3 = 11
Let's look back.
First: first terms.
Then: take away 3 each time.
Then: the formula.
Last: check.
Answer
an = 20 − 3n