How_To_Be_Good_At_Math

Formulas and sequences

Simple sequences

To find the formula for any sequence, we

need to look at the pattern. Some sequences

have an obvious pattern, so we can easily find

the rule and write it as a formula.

Finding terms

The formula to work out the nth

term in this sequence is 6n + 2.

Can you continue the sequence

and apply the formula?

TRY IT OUT

Answers on page 320

Two-step formulas

Some sequences will follow two steps

such as multiplying and subtracting,

or multiplying and adding.

The rule is multiply

the term by 4

The rule is multiply

the term by 5, then

subtract 1

+4

+5

+4

+5

+4

+5

+4

16,

19,

12,

14,

8,

9,

4,

4,

20,

24,

5th term

5th term

4th term

4th term

3rd term

3rd term

2nd term

2nd term

1st term

1st term

n = 5

4n = 20

n = 5

5n − 1 = 24

n = 4

4n = 16

n = 4

5n − 1 = 19

n = 3

4n = 12

n = 3

5n − 1 = 14

n = 2

4n = 8

n = 2

5n − 1 = 9

n = 1

4n = 4

n = 1

5n − 1 = 4

This sequence is made up of the

multiples of 4. So, we can say

the nth term is 4 × n. In algebra,

we write this as 4n.

The formula for this sequence is 5n − 1.

So, to find any term in the sequence, we

have to perform a multiplication followed

by a subtraction.

To find the 50th term in the sequence,

for example, we replace n in the formula

with 50. Then we can write 5 × 50 − 1 = 249.

So, the 50th term is 249.

So, to find the value of the 30th term

for example, we simply replace n

in the formula with 30 and perform the

calculation 4 × 30 = 120.

8, 14, 20, 26, 32, 38, ...

...
...

Write the next

five numbers

in this sequence.

Calculate

the value of

the 100th term.

Calculate

the value of

the 40th term.

+5

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