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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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 = ar^n-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 3^rd term, we need to know the r apart from the given “a” first term

T4 → 108 =4r^4-1

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

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