SIKONGO BOARDING SECONDARY SCHOOL
DEPARTMENT OF MATHEMATICS
ADDITIONAL MATHEMATICS 4030
ECZ EXAM PRACTICE QUESTIONS ON ARITHMETIC & GEOMETRIC PROGRESSIONS-2026
1
2
8
(a) The third and sixth terms of a geometric progression are 2 3 and 81 respectively. Find
(i)
(ii)
the common ratio and the first term,
the sum to infinity of the geometric progression.
[3]
[2]
(b) The nth term of an arithmetic progression is 4𝑛 + 1. Find, in terms of n, the sum of the
first n terms of the progression.
[4]
2
(a) The eighth term of an arithmetic progression is four times the fifth term and the sum of
the first eight terms is 20. Calculate the sum of the first ten terms.
[5]
1
4
(b) The second and the fifth terms of a geometric progression are 18 and 243 respectively.
Find
(i) the common ratio and the first term,
[3]
(ii) the sum to infinity of the progression.
[2]
[2016 P2 G12]
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3
(a) The sum of the first four terms of an arithmetic progression is 62 and the second term is
17. Find
(i)
the first term and the common difference,
[3]
(ii)
the sum of the first 40 terms.
[2]
(b) A geometric progression is given by 81, 54, 36, …Find
4
1|Page
(i)
the 20th term,
[2]
(ii)
the sum to infinity.
[2]
(a) An agent sponsoring students decids to give a sum of money to a school each year 12
years. The agent decides to give K75 000.00 in the first year and to increase the
sponsorship by K10 000.00 each year.
(i)
Find the amount the agent gives out in the twelfth year.
[3]
(ii)
Find the amount received by the school from the agent altogether.
[3]
7
(b) The first term of a geometric progression is 1 and the sum of the first 3 terms is 9 . Find
the two possible values of the common ratio of this series.
[4]
[2017 2 G12 CE]
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5
(a) The sum of the first 6 terms of a arithmetic progression is 57 and the sum of the next 7
terms is 203. Find the
(i)
first term and the common difference,
[3]
(ii)
sum of the first 12 terms of the progression.
[2]
1
(b) The third term of a geometric progression is 32 and the ninth term is 2 . Find the
6
(i)
first tem and the common ratio,
[3]
(ii)
sum to infinity.
[1]
(a) In an arithmetic progression, the 5th term is three times the second term. The sum of the
first ten terms is 50. Find the first term and the sum of the first 30 terms.
[6]
(b) The fifth term of a geometric progression is 8, the third term is 4 and the common ratio is
positive. Find the first term, the common ratio and the sum of the first twelve terms.
[4]
[2017 P2 G12]
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8
(a) The 14th term of an arithmetic progression is 55 and the sum of the first 13 terms is
351.find the sum of the first 28 terms.
1
(b) A geometric progression has a common ratio of 3 and the sum of the first four terms is
8
. Find the
27
9
(i)
first term of the geometric progression.
[2]
(ii)
sum to infinity.
[2]
(a) The first and last terms of an arithmetic progression are 3 and 95 respectively. The sum
of all the terms is 1176. Calculate
(i)
number of terms in the progression,
[2]
(ii)
the common difference,
[2]
(iii)
the sum of the first 12 terms in the progression.
[2]
5
(b) The first term of a geometric progression is 2 and the common is 2 . Find the least
number of terms which can be added for the sum not to exceed 800.
[2018 P2 G12]
2|Page
[4]
10
(a)
(b)
The last term of a arithmetic progression of 20 terms is 195 and the common
difference is 5. Find
(i)
the first term,
[2]
(ii)
the sum of the arithmetic progression.
[2]
The sum to infinity of a geometric progression is 3 and the sum of the first two terms is
2
2 3. Given that 𝑟 > 0, find the first term and common ratio of the geometric progression.
[5]
(c)
In an arithmetic progression, the 15th term is double the 9th term. If the sum of the first 9
terms is 279, find the first term and the common difference.
[5]
b)
1 + 𝑚, 3𝑚 + 1 and 1 + 4𝑚, where 𝑚 ≠ 0, are the first three terms of a geometric
progression. Find
(i)
the value of m,
[2]
(ii)
the common ratio,
[1]
iii)
the sum to infinity of the progression.
[2]
[2018 P2 G12]
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11
(a)
In an arithmetic progression, the 22nd term is 4 times the 5th term and the 12th term is
more than the 8th term. Find
(i)
the first term and the common difference.
[3]
(ii)
the sum of the first 15 terms of the progression.
[2]
(b)
Given that the sum to infinity of a geometric progression is 36 and the sum of the first
81
three term is 2 , find the first term and the common ratio.
[4]
(c)
An arithmetic progression contains 20 terms. Given that the 6th term is 17 and the sum of
the firs 8 terms is 100, calculate the sum of the last 8 terms.
[5]
(d)
The 3rd term and the 5th term of a geometric progression are 1 5 and 125 respectively. Find
3
32
(i)
the first term and the common ratio,
[3]
(ii)
the sum to infinity of the progression.
[2]
[2019 P2 GCE]
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12
(a)
5
(i)
3|Page
1
If the 3rd and 6th terms of an arithmetic progression are 16 and 5 respectively, find the
first term and the common difference,
[3]
(ii)
(b)
10th term.
[2]
The first terms of a geometric progression are 3𝑥 + 5, 8 ,2. Find the
(i)
common ratio and the value of 𝑥,
[3]
(ii)
sum to infinity.
[1]
(c)
In an arithmetic progression, the 15th term is twice the 9th term. The sum of the first 15
terms and the sum of the first 9th terms added together is 279. Find the first term and the
sum of the first 40 terms.
[6]
(d)
The seventh term of a geometric progression is 27, the fifth term is 3 and the common ratio
is positive. Find the first term, the common ratio and the sum of the first 8 terms. [4]
[2019 P2 G12]
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13
(a)
If 3𝑥 − 1, 2𝑥 − 2 and 𝑥 − 1, (𝑥 > 0) are the first three terms of a geometric progression,
find
(i)
the value of 𝑥,
[2]
(ii)
the common ratio,
[1]
iii
the sum to infinity.
[2]
(b)
There are 20 terms in an arithmetic progression. The sum of the first 10 terms is 55 and the
sum of the last 10 terms is 355. Find the first term and the common difference.
[3]
(c)
An arithmetic progression has 15 terms and the last term is 44. The sum of the last terms
is 305. Find the first term and the common difference.
[5]
(d)
The third and sixth terms of a geometric progression are 5 and 625 respectively. Find
36
972
(i)
the first term and the common ratio,
[3]
(ii)
the sum to infinity.
[2]
[2020 P2 GCE]
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14
1
(a)
The nth term of an arithmetic progression is given by 𝑇𝑛 = 2 (4𝑛 − 3). Find the first term,
the common difference and the sum of the first 50 terms.
[4]
(b)
In a geometric progression, the 2nd and 7th terms are 40 2 and 6 respectively. Find the first
1
1
term, the common ratio and the sum of the first 10 terms.
[5]
[2020 P2 G12]
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4|Page
15
(a)
5
1
If the 4th and the 8th terms of an arithmetic progression are 14 and 14 respectively, find the
sum of the first 20 terms.
[4]
(b)
In a geometric progression, the product of the 1st and 7th terms is equal to the 4th term while
the sum of the 1st and 4th terms is equal to 28. Find the sum of the first 5 terms.
[5]
[2021 P2 G12]
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16
(a)
(b)
In an arithmetic progression, the sum of the first 5 terms is 50 and the sum of the next 10
terms is 325. Find
(i)
the first term and the common difference,
[3]
(ii)
the sum of the first 13 terms of the progression.
[1]
A doctor earns an annual salary of K4 000.00 during the first year of practice. In each
succeeding year, the annual salary increases by 10%.
(i)
Find the sum of the doctor’s annual salaries over the first 6 years.
[2]
(ii)
Find the number of years the doctor must work, if the sum of his annual salaries is
to exceed a million kwacha.
[3]
[2021 P2 GCE]
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17
(a)
(b)
The sum of the first 6 terms of an arithmetic progression is 18 and the sixth term is two
times the third term. Find the
(i)
first term and the common difference,
[3]
(ii)
sum of the first ten terms.
[2]
The ninth term of a geometric progression is 32, the seventh term is 16 and the common
ratio is positive. Find
(i)
the first term,
[2]
(ii)
the sum of the first ten terms.
[2]
[2022 P2 GCE]
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18
(a)
5|Page
The fourth term and the twenty second term of an arithmetic progression are 4 and 5
respectively. Find the
(i)
first term and the common difference,
[3]
(ii)
fortieth term of the progression.
[2]
(b)
The second and fourth terms of a geometric progression are 20 and 12.8 respectively. Given
that all the terms are positive, find the sum
(i)
of the first 7 terms,
[3]
(ii)
to infinity of the progression.
[1]
[2022 P2 G12]
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19
(a)
(b)
The last term of an arithmetic progression of 18 terms is 136 and the common difference
is 6. Find the
(i)
first term,
[1]
(ii)
sum of the progression.
[2]
The first term of a geometric progression is 4 and the common ratio is 0.2. Find the
(i)
sum to infinity,
[2]
(ii)
least value of n terms which differ from the sum to infinity by less than 0.004.[4]
[2023 P2 GCE]
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20
(a)
(b)
The 12th term of an arithmetic progression is 30 and the 20th term is 78. Find the
(i)
first term and the common difference,
[3]
(ii)
number of terms whose sum is 90.
[3]
35
14
The sum of the first two terms of a geometric progression is 2 and the third term is 3 ,
where 𝑟 > 0. Find the value of the common ratio.
[3]
[2023 P2 G12]
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21
(a)
In an arithmetic progression, the sum of the first twelve terms is 282, and the sum of the
first fourteen terms is 357. Find the 7th term.
[5]
(b)
The 1st , 2nd and 3rd terms of a geometric progression are 𝑦 + 5, 𝑦 and 𝑦 − 4 respectively.
Calculate the
(i)
value of 𝑦,
[2]
(ii)
common ratio.
[2]
[2024 P2 GCE]
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6|Page
22
(a)
(b)
The seventh term of an arithmetic progression is 41 and the thirteenth term is 77. Find the
(i)
first term and the common difference,
[3]
(ii)
twentieth term.
[2]
1
The fourth term of a geometric progression is 1, the eighth term is 256 and the common
ratio is positive. Find the
(i)
first term and the common ratio,
[3]
(ii)
tenth term.
[2]
[2024 P2 G12]
____________________________________________________________________________________
23
(a)
The 31st term of an arithmetic progression is 83 and the sum of its first 51 terms is 3 468.
Find the first term and common difference.
[4]
(b)
The 2nd and 5th terms of a geometric progression are 21 and 567 respectively. Find the
10
80
(i)
first term and common ratio,
[3]
(ii)
sum to infinity of the progression.
[2]
[2025 P2 GCE]
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24
(a)
An arithmetic progression has 241 terms and a common difference of 0.1. Given that the
sum of all the terms is 964, find the first term and the sum of the first 41 terms. [5]
(b)
A new geometric progression is formed by squaring each of the terms of the progression
with the first term 6 and a sum to infinity of 18. Find the sum to infinity of the new
geometric progression.
[4]
Set your pace to a stroll. Stop whenever you want. Interrupt, jump back and
forth, I won’t mind. These mathematical problems must be as easy as laughter.
They are stuffed with small things to take away. Please help yourself-masumo
nchimunya 2026
7|Page