Sharp Sharp: Gain Admission into 200 Level to Study in any Course in any University of Your Choice. NO JAMB | LOW FEES. Registration is in Progress. For more details, call: 0706 664 6818 or CLICK HERE

HURY NOW: Live, Work, and STUDY in Canada or any other country ABROAD with no stress. No payment until your visa is approved. CLICK HERE for more details or WhatsApp 09019196619

# Geometric Progression (GP) | JAMB Free Tutorial for Maths

19 Shares

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.

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.
• This page is also suitable for candidates writing other exams like WAEC/NECO/NABTEB etc.
• If after reading this tutorial YOU HAVE ANY questions on this topic, please feel free to ask us using the comment box below.
• Have you heard of Allschool VIP JAMB Online Lesson? The Lesson is strictly based on JAMB Syllabus, which means our teachers focus on the exact things that will most likely come out in JAMB. Joining the Lesson is one of the surest ways to score high in JAMB. Click here to see how to join and other details.

## GEOMETRIC PROGRESSION (G.P)

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

Solution1

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

### SUM OF A GP TO INFINITY (S∞ )

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

Thus

S∞  = 8/1-0.5

= 8/ 0.5

= 16

### EXERCISES ON GP

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.

In Allschool VIP JAMB Online Lesson, our teachers focus on the exact things that will most likely come out in JAMB. Joining the Lesson is one of the surest ways to score high in JAMB. Click here to see how to join and other details.

### Recommended Articles

AllSchool Team.

19 Shares

Stories You Shouldn't Have Missed:

Subscribe
Notify of
Inline Feedbacks

Pls sir i did u got the answer

Pls sir I did u got the a answer

(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

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 
Thank you all

Comment… This was great

A)2/3
B)-2/5
C)72/25

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

1.A 2/3
2.B -2/5
3.C 72/25
09065835446

Comment…1=a 2=c 3=a

1=2/3
2=-2/5
3=72/25

08036797945
1.c-2
2.c2
3.a8/3

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

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

19
0