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Geometric Progression (GP) | Free JAMB Tutorial on 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.
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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

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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

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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

Qudus

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

Tolulope

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

Lateef

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

Farouq

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

ayomide

Comment…1=a 2=c 3=a

Alenu faith

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

Aisha Hussain Adam

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

Olawale

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

08078337922

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

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