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Geometric Progression (GP) | JAMB Free Tutorial for Maths

Today on our JAMB UTME Free Tutorial, will treat mathematics and our topic is Geometric Progression (G.P). We will give examples and exercises.

In our previous post on our JAMB FREE TUTORIAL, we taught Arithmetic Progress (AP). We started by explaining the series and sequence. If you missed the post, please check it out by CLICKING HERE.

Today, we will teach you everything you need to know about Geometric Progression. Please note that if you have any questions/problems, the Mathematics tutor Oguguo J.C, will be very pleased to attend to them, just use the comment box below and the question will be solved.

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Before we proceed, please TAKE NOTE of the following:

  • We strongly recommend you take your time and read this topic. You can read it again and again.
  • Make sure you attempt all the exercises on this page. Use the comment box to tell us the answers.
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A geometric progression or exponential sequence is a form of sequence that has a common ratio between any of the terms and its preceding one

Example 1

  • 2, 4,8,…

We observe that the common ratio here is 4/2 = 8/4 given rise to the common ratio (r) = 2

In summary, the general term of a GP is in the form of a, ar2, ar3, …, arn  thereby given rise the general term of a GP to be Tn = arn-1

Example 2

  • Determine the third term of a geometric progression whose first and fourth term are 4 and 108 respectively


To determine the 3rd term, we need to know the r apart from the given “a” first term

T4 → 108 =4r4-1

108 = 4r3

108/4 = r3

Raise both sides to the same power

33 = r3

3 = r

Thus, T3 = 4(3)3-1

= 36


A GP whose common ratio is between  -1 and +1 say -1/2, 1/2, -1/4, ¼ etc has sum which approaches a finite value as n approaches infinity. It is given as

S= a/1 – r

Example 2

The first and sixth term of a GP are 8 and ¼ respectively. What is its sum to infinity?

Solution 2

S= a/1 – r

r can be gotten from T6 → ¼ = 8(r)5

multiply through by 1/8

1/32  = r5

Raise both sides to the same powers

(1/2)5  =r5

Equating terms

½ = r


S∞  = 8/1-0.5

= 8/ 0.5

= 16


The exercises are:

  1. Evaluate ( 1/2, -1/4 + 1/8 – 1/16 + …) – 1
    a) 2/3 b) 0 c) -2/3 d) -1
  2. The first term of a GP is 350. If the sum to infinity is 250, find the common ratio
    a) -5/7 c) -2/5 c) 2/5 d) 5/7
  3. The first term of a GP is twice its common ratio. Find the sum of the first two terms of the progression. If its sum to infinity is 8
    a) 8/5 b) 8/3 c) 72/25 d) 46/9

NOTE: If YOU HAVE ANY QUESTION on this topic, please feel free to ask us using the comment box below. If this page was also helpful, please let us know using the comment box below.

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AllSchool Team.

Thank you so much for reading. We will appreciate it if you share this with your loved ones.

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Uduakhomo iwhemoisa

Pls sir i did u got the answer

Uduakhomo iwhemoisa

Pls sir I did u got the a answer

Uduakhomo iwhemoisa

(1)d, (2)d, (3)b


How can I solve this?
A GP has a first term of “a” and a common ratio of “r” and its 6th term is 786.Another GP has a first term of “a”, a common ratio of 6r and its 3rd term is 3466.Find a and r

Oguguo Chidiebere

The answers to the GP exercises are
1. C(-2/3)
2. C(-2/5)
3. C(72/25)
And the first winner for the GP exercises
is [08078337922]
Thank you all

Peter Anointed Mmesoma

Comment… This was great

OGUGUO Chidiebere

Keep the answers coming




1. 2/3
2. -2/5 or 0.4
3. 72/25


1.A 2/3
2.B -2/5
3.C 72/25


Comment…1=a 2=c 3=a

Alenu faith


Aisha Hussain Adam



1. -2/3 (c)
2. -2/5 (b)
3. 72/25 (c)

Unique Ezike

Comment…please am sori to ask dis buh am worried plz is there no platform for arts student


1. -2/3. C. 2. c. -2/5 c. 3. 72/25. c

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