3, 7, 11, 15, ..., find the 10th term Step by Step

Step by step

The question

Question: 3, 7, 11, 15, …: find term 10.

A sequence is a list of numbers in order.

3, 7, 11, 15, ...

1 Find the difference

We add 4 every time.

A list like this is an arithmetic sequence.

The number we add is called the difference: d = 4.

d = 4

2 Find the rule

Term 1 is 3.

a₁ = 3

a₁ is term 1, a₂ is term 2.

So aₙ is term number n.

a_n = term number n

Term 2: we add 4 one time.

a₂ = 3 + 1 × 4

Term 3: we add it two times.

a₃ = 3 + 2 × 4

We add 4 one time less than the term number.

times we add 4 = term number − 1

So for term n, we add 4, (n − 1) times.

a_n = 3 + (n − 1) × 4

This rule works for every arithmetic sequence: the first term, plus (n − 1) times the difference.

a_n = a₁ + (n − 1) × d

3 Find term 10

For term 10, n is 10.

We put 10 in place of n.

a₁₀ = 3 + (10 − 1) × 4

Brackets come first.

Order: ( ) → x² √ → × ÷ → + −

10 minus 1 is 9.

= 3 + 9 × 4

Times comes before plus.

9 times 4 is 36.

= 3 + 36

3 plus 36 is 39.

a₁₀ = 39

So term 10 is 39.

4 Check

Let's check the rule with a term we know.

Put n = 4.

a₄ = 3 + (4 − 1) × 4 = 3 + 3 × 4 = 3 + 12

= 15

We get 15.

That is term 4 in the list.

So the rule is right!

Let's look back.

First: find the difference.

Then: find the rule.

Then: find term 10.

Last: check.

Answer