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Chapter 1 - SEQUENCE

1) Sequences can be arithmetic or geometric. Arithmetic sequences have a common difference while geometric sequences have a common ratio. 2) The formulas to find the nth term (Tn) of an arithmetic sequence is Tn = a + (n-1)d, and the formula to find the sum of the first n terms (Sn) is Sn = (n/2)(2a + (n-1)d). 3) The formulas to find the nth term (Tn) of a geometric sequence is Tn = arn-1, and the formula to find the sum of the first n terms (Sn) is Sn = (a(rn -

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460 views24 pages

Chapter 1 - SEQUENCE

1) Sequences can be arithmetic or geometric. Arithmetic sequences have a common difference while geometric sequences have a common ratio. 2) The formulas to find the nth term (Tn) of an arithmetic sequence is Tn = a + (n-1)d, and the formula to find the sum of the first n terms (Sn) is Sn = (n/2)(2a + (n-1)d). 3) The formulas to find the nth term (Tn) of a geometric sequence is Tn = arn-1, and the formula to find the sum of the first n terms (Sn) is Sn = (a(rn -

Uploaded by

Airin Samuel
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1

Chapter 1: SEQUENCE
Madam Nowyannie Willie D. Tamsin
13 OCTOBER 2020
2

▪ Sequence
❖ a list of terms formed according to a
certain fixed rule – arranged in a
specified order.
❖Order in which events happen.

INTRODUCTION ▪ Certain words can be sequence “clues.”


❖Time-Order Words:
* first, next, then, finally
* yesterday, today, tomorrow
3
4

▪ Have the same difference, d, throughout


the sequence.
▪ d – known as common difference
– obtained by subtract the 2
consecutive terms.
- at least 2 common difference

ARITHMETIC
d = T2 − T1 = T3 − T2
SEQUENCE
▪ Some examples:
a) 2,4,6,8,…
b) -5,-10,-15,-20,…
c) 3,10,17,24,…
5

Arithmetic sequence
▪ a- first term
d- common difference
n- number of terms
Tn - nth term

▪ Finding the nth term,


𝑇𝑛 = 𝑎 + 𝑛 − 1 𝑑

▪ Finding the sum of the first nth term,

𝑛
𝑆𝑛 = 2𝑎 + 𝑛 − 1 𝑑
2
6

▪ Have the same ratio throughout the


sequence (a.k.a common ratio,r).
▪ r - common ratio T2 T3
r= =
Geometric ▪ Some examples: T1 T2
Sequence a) 3,9,27,81,…
b) -5,10,-20,40,…
c) 20,10,5,5/2,…
7

▪ a - first term
T2 T3
r= =
r - common ratio T1 T2
▪ Finding the nth term,

𝑇𝑛 = 𝑎𝑟 𝑛−1
Geometric
▪ The sum of the first nth term is given by
Sequence
𝑎 𝑟𝑛 − 1
𝑆𝑛 =
𝑟−1
8

i. Identidy the type of sequence.


How? – By finding the common difference/
Tips to answer common ratio.
question on ii. Focus on the given formula.
Sequence iii. Identify the keyword (is it term or sum)
iv. Answer the question.
9

DEGREE
10

DEC 2019 (No. 1)


Monthly expenses for raising a child increased by RM8.50 from previous
month. If the expenses for the first month was RM32, compute the total
expenses after 30 months? (5 marks)

Answer:
𝑆30 = 4657.50
11

JUNE 2019 (No. 1)


A mall gives a lucky draw number to all customers who made a purchase more than RM250
in one receipt. The lucky draw numbers given to the customers will follow the sequence:

1000, 1500, 2000, …

What is the lucky draw number received by the 900th customer? (5 marks)

Answer: 𝑇900 = 450500


12

DEC 2018 (No. 1)


Given the 5th term of a geometric sequence is 3,240 with a
common ratio of 3. Find the sum of the first 10 terms. (5 marks)

Answer: 𝑆10 = 1180960


13

JUNE 2018 (No. 1)


The current price of an item is RM600. The price of the item increases by 8%
each month.What will be the price of the item after 20 months. (5 marks)

Answer: 𝑇20 = 2589.42


14

JAN 2018 (No. 1)

𝑟=3
Answer: 𝑆7 = 2186
15

JULY 2017 (No. 1)

𝑑 = −3
Answer: 𝑆12 = 858
16

December 2016 (No. 1)

𝑎 = 10
𝑑=4
Answer: 𝑆30 = 2040
17

JUNE 2016 (No. 1)

𝑟 = 1.02
Answer: 𝑇 = 7.40
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18

DEC 2014 (No. 3(c))

3
Answer: i) 𝑟 = 4 , 𝑛 = 9
ii) 𝑆9 = 14.80
19

JUNE 2014 (No. 3(c))

Answer: 𝑟 = 1.05,
𝑇20 = 416946.78
20

DIPLOMA
21

Mac 2016, Part A (No. 1)

Answer: 𝑑=3
𝑆50 =3275
22

Mac 2015, 3 (a)

Answer:
1
𝑖) 𝑟 = , 𝑎 = −768
2
𝑖𝑖) 𝑆50 = 3275
23

Sept 2013, 3 (a)


(b)

Answer:
(a) n=18
(b) (i) 𝑇6 = 38288.45
(ii) 𝑆12 = 477513.80
24

Mac 2013, 3 (a),


(b)

Answer:
(a) n=40
(b) a=15, r=-2

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