#### Topic Content:

- Meaning of Sequence (Examples)

### What is a Sequence?

A sequence is an arrangement of numbers that follows a particular pattern or rule e.g. 3, 7, 9, 11, 15… The rule here is that you add 4 to each term.

### Example 1.1.1:

Find the next three terms of these sequences. Write down the rule for each sequence.**(i)** 4, 9, 14, 19, 24**(ii)** 0.25, 0.28, 0.31, 0.34, 0.37…**(iii)** 4, -1, -6, -11, -16…

**Solution**

**(i)** 4, 9, 14, 19, 24, 29, 34, 39 |** rule = add 5**

**(ii)** 0.25, 0.28, 0.31, 0.34, 0.37, 0.40, 0.43, 0.46 | **rule = add 0.03**

**(iii)** 4, -1, -6, -11, -16, -21, -26, -31 | **rule = add -5**

### Example 1.1.2:

Find a formula for the nth term of the sequences in example 1 above and use your formula to find the 20^{th} term for each.

**Solution**

**(i)**Â d = 5, a = 4

since the rule is by adding 5

nth term is given by:

â‡’ 5_{n} = 5, 10, 15, 20, 25

the sequence = 4, 9, 14, 19, 24

the difference = 1 1 1 1 1

The formula is given as 5n – 1

20^{th} term = 5 Ã— 20 – 1 = 100 – 1

= 99

**(ii)** rule is add 0.03

â‡’ 0.03n = 0.03Â 0.06Â 0.09Â 0.12Â 0.15

the sequence = 0.25 0.28 0.31 0.34 0.37

difference = 0.22 0.22 0.22 0.22 0.22

Formula = 0.03n + 0.22

or = \( \frac{3n + 22}{100}\)

20^{th} term = 0.03 Ã—Â 20 + 0.22

= 0.6 + 0.22

= 0.82

**(iii) **the rule is add -5

â‡’ -5n = -5Â -10Â -15Â -20Â -25

the sequence = 4 -1 -6 -11 -16

the difference = 9 9 9 9 9

Formula = -5n + 9

20^{th} term = -5 Ã— 20 + 9

= -100 + 9

= -91

### Example 1.1.3:

Find the 6^{th }and 24^{th} terms of the following**(i) **6n – 3n^{2 }Â **(ii)** \( \frac{5n \;-\; 3}{4}\)

**Solution**

**When n = 6**

**(i)**Â 6n – 3n^{2 }= 6 Ã— 6 – 3(6^{2})

= 36 – 3(36)

i.e. 6n^{2 }– 3n^{2 }= 36 – 108

= -72

**When n = 24**

6n – 3n^{2 }= 6 Ã— 24 – 3(24^{2})

= 144 – 3(576)

= 144 – 1728

6n – 3n^{2}= -1584

**(ii)** \( \frac{5n \;-\; 3}{4}\)

**when n = 6**

\( \frac{5n \;-\; 3}{4}\) = \( \frac{5 \; \times \; 6 \;-\; 3}{4}\)

= \( \frac{30 \;-\; 3}{4}\)

= \( \frac{27}{4}\)

= \( \scriptsize 6 \normalsize \frac{3}{4} \scriptsize \; or \; 6.75\)

**When n = 24**

= \( \frac{120 \;-\; 3}{4}\)

= \( \frac{117}{4}\)

= \( \scriptsize 29 \normalsize \frac{1}{4}\scriptsize \; or \; 29.25\)

Well illustrated step by step examples.Bravo!

Understandable

Keep up the good work

i dont get how you got the differences

1st sequence: 5, 10, 15, 20, 25

2nd sequence: 4, 9, 14, 19, 24

difference: 5-4, 10-9, 15 – 14, 20 – 19, 25 – 24

= 1, 1, 1, 1, 1