Step by step
The question
Question: 5, 8, 11, 14, …: find term 20.
A sequence is a list of numbers in order.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Find the difference
From 5 to 8, we add 3.
From 8 to 11, we add 3 again.
We add 3 every time.
A list like this is an arithmetic sequence.
The number we add is called the difference: d = 3.
2 Find the rule
Term 1 is 5.
a₁ is term 1, a₂ is term 2.
So aₙ is term number n.
Term 2: we add 3 one time.
Term 3: we add it two times.
We add 3 one time less than the term number.
So for term n, we add 3, (n − 1) times.
This rule works for every arithmetic sequence: the first term, plus (n − 1) times the difference.
3 Find term 20
For term 20, n is 20.
We put 20 in place of n.
Everyone uses the same order, so we all get the same answer.
Brackets come first.
20 minus 1 is 19.
Times comes before plus.
19 times 3 is 57.
5 plus 57 is 62.
So term 20 is 62.
4 Check
Let's check the rule with a term we know.
Put n = 4.
We get 14.
That is term 4 in the list.
So the rule is right!
5 Pick the choice
Our answer is a₂₀ = 62.
That is choice B.
6 Why not the others
A is 57.
Wrong: 19 × 3: forgot to start from 5.
C is 65.
Wrong: 20 jumps of 3: the 20th term is 19 jumps after the first.
D is 100.
Wrong: 20 × 5: multiplied the first term.
Let's look back.
First: find the difference.
Then: find the rule.
Then: find term 20.
Then: check.
Then: pick the choice.
Last: why not the others.