This free online revision course is specially compiled for students to revise important topics from A Level H2 Maths. The course content is presented in an easy to study format with 5 essential questions, core concepts and explanation videos for each question. Gain access to the FREE video explanation at https://timganmath.edu.sg/a-level-free-h2-math-notes-and-resources/arithmetic-and-geometric-progressions/

1. Topical Worksheet: Arithmetic and Geometric Progressions
1 | Mastering H2 Math with the Best Learning Resources www.timganmath.edu.sg
ARITHMETIC AND GEOMETRIC PROGRESSION
The terms of a geometric progression 1 2 3 4
, , , ,...
u u u u are such that the sum to infinity is 81 and the sum of the
first 4 terms is 80.
If 1 100
u  and n 3
 ,
(i) find n
u in terms of n , [5]
(ii) show that 3 4 5
1
... 1
3
n q
n
u u u u p
+
 
 
+ + + + = − −
 
 
 
 
 
, where the integers p and q are to be found. [3]
Answers: (i)
1
1
108
3
n
n
u
−
 
= −
 
 
(ii)
2
1
9 1
3
n−
 
 
− −
 
 
 
 
 
An arithmetic series has first term
3
2
and fourth term 4
u .
A geometric series also has first term
3
2
and fourth term 4
u .
Given that the common ratio of the geometric series is non-negative and the sum of its first 3 terms is
21
2
, find
the sum of the first 10 odd-numbered terms of the arithmetic series. [5]
Answer: 330
The curve C has equation 3
y kx
= . The tangent at the point P on C meets the curve again at point Q . The
tangent at point Q meets the curve again at point R . If the x -coordinates of P , Q and R are p , q , and r
respectively where 0
p  .
(i) Show that p and q satisfy the equation
2
2 0
q q
p p
   
+ − =
   
   
. [4]
(ii) Show that p , q , and r are three consecutive terms of a geometric progression. Hence determine if this
geometric series is convergent. [4]
[You may use the identity ( )( )
3 3 2 2
a b a b a ab b
− = − + + for ,
a b .]
2009 VJC J1 MYE Q10
2020 RI P2 Q1
2017 TJC P1 Q5

2. Topical Worksheet: Arithmetic and Geometric Progressions
2 | Mastering H2 Math with the Best Learning Resources www.timganmath.edu.sg
A fund is started at $6000 and compound interest of 3% is added to the fund at the end of each year. If
withdrawals of $k are made at the beginning of each of the subsequent years, show that the amount in the fund
at the beginning of the ( )
1
n+ th year is
( )( )
100
$ 180 1.03
3
n
k k
 
− +
 
[5]
(i) It is given that 400
k = . At the beginning of which year, for the first time, will the amount in the fund
be less than $1000? [2]
(ii) If the fund is fully withdrawn at the beginning of sixteenth year, find the least value of k to the nearest
integer. [2]
Answers: (i) 19th
year (ii) $503
Jane deposited $ x on 1 January 2018 and then a further $ x on 1 February 2018 and at the start of every
subsequent month in a bank account. The interest rate was 0.3% per month, so that on the last day of each
month the amount in the account on that day was increased by 0.3% .
(i) Find an expression in terms of n and x for the amount of money in the bank account on the last day of
the n th month. [3]
(ii) What is the minimum amount (to the nearest dollar) Jane should deposit in the bank every month if she
were to have at least $5000 in the bank at the end of 15 months? [2]
After 2 years, Jane stopped depositing $ x per month, and instead decided to withdraw $ 200 from the account
on the th
15 of every subsequent month, starting on th
15 January 2020. The interest rate remained as 0.3% per
month, so that on the last day of each month the amount in the account on that day was increased by 0.3% .
(iii) Using the value of x found in part (ii), find the date in which Jane would do her last withdrawal till she
has no more money left in her account, and the amount of her last withdrawal to the nearest cent. [5]
Having no money left in her bank account, Jane decided to take an interest free loan of $ 10000 from a friend.
She would repay her friend $ 100 on the last day of the first month she took the loan. On the last day of each
subsequent month, she would repay her friend $ 150 more than the amount she repaid in the previous month.
(iv) Find the number of months Jane will take to repay her loan. [2]
Answers: (i) ( )
1003
1.003 1
3
n
 − (ii) $326 (iii) July 2023;$48.77 (iv) 12 months
2017 JJC P1 Q4
2021 HCI J1 CT1 Q5