Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev

Quantitative Aptitude for Banking Preparation

SSC : Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev

The document Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev is a part of the SSC Course Quantitative Aptitude for Banking Preparation.
All you need of SSC at this link: SSC

Geometric Progression

A series in which each preceding term is formed by multiplying it by a constant factor is called a Geometric
Progression G. P. The constant factor is called the common ratio and is formed by dividing any term by the
term which precedes it.

In other words, a sequence, Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev is called a geometric progression

If Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev = constant for all n ∈ N.


The General form of a G. P. with n terms is a, ar, ar2,…arn -1
Thus if a = the first term
r = the common ratio,
Tn = nth term and
Sn = sum of n terms
 

General term of GP = Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev


Ex.1 Find the 9th term and the general term of the progression.
Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev

Sol. The given sequence is clearly a G. P. with first term a = 1 and common ratio = r = Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev

Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRevGeometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev

Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev


Sum of n terms of a G.P:

Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev

Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev

Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev


Sum of infinite G.P:
If a G.P. has infinite terms and -1 < r < 1 or |x| < 1, then sum of infinite G.P is Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev


Ex.6 The inventor of the chess board suggested a reward of one grain of wheat for the first square, 2
 grains for the second, 4 grains for the third and so on, doubling the number of the grains for
 subsequent squares. How many grains would have to be given to inventor? (There are 64
 squares in the chess board).

 

Sol. Required number of grains
= 1 + 2 + 22 + 23 + ……. To 64 terms =  Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev


Recurring Decimals as Fractions.
If in the decimal representation a number occurs again and again, then we place a dot (.) on the number and
read it as that the number is recurring.
e.g., 0.5 (read as decimal 5 recurring).
This mean 0.Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev = 0.55555…….∞

0. 4 Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev = 0.477777……∞


These can be converted into fractions as shown in the example given below


Ex.7 Find the value in fractions which is same as of Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev

Sol. 

Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev


Properties of G.P.


I. If each term of a GP is multiplied or divided by the same non-zero quantity, then the resulting sequence
is also a GP.
For example: For G.P. is 2, 4, 8, 16, 32…


Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev


II. SELECTION OF TERMS IN G.P.
Sometimes it is required to select a finite number of terms in G.P. It is always convenient if we select the
terms in the following manner :

Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev

If the product of the numbers is not given, then the numbers are taken as a, ar, ar2, ar3, ….

 

III. Three non-zero numbers a, b, c are in G.P. if and only if
b2 = ac     or         Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev
b is called the geometric mean of a & c


IV. In a GP, the product of terms equidistant from the beginning and end is always same and equal to the
product of first and last terms as shown in the next example.

Geometric Progression - Examples (with Solutions), Algebra, Quantitative Aptitude GMAT Notes | EduRev

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Complete Syllabus of SSC

SSC

Dynamic Test

Content Category

Related Searches

Summary

,

Exam

,

Free

,

Algebra

,

ppt

,

Quantitative Aptitude GMAT Notes | EduRev

,

Quantitative Aptitude GMAT Notes | EduRev

,

Semester Notes

,

MCQs

,

Extra Questions

,

Important questions

,

shortcuts and tricks

,

Geometric Progression - Examples (with Solutions)

,

Objective type Questions

,

Viva Questions

,

Geometric Progression - Examples (with Solutions)

,

Geometric Progression - Examples (with Solutions)

,

practice quizzes

,

Sample Paper

,

Previous Year Questions with Solutions

,

video lectures

,

Quantitative Aptitude GMAT Notes | EduRev

,

study material

,

Algebra

,

pdf

,

mock tests for examination

,

Algebra

,

past year papers

;