CAT Quantitative Aptitude Sequence & Series: Know Basic Concept, Important Formulas and Solved Questions
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The topic sequence and series from CAT Quantitative Aptitude can get you around 3 to 6 marks in the upcoming examination. The difficulty level of this topic can be considered moderate, however, with regular practice and knowledge of direct formulas candidates can solve the questions from the topic very easily. Check CAT 2021 Quantitative Aptitude Syllabus
In this article, we have added all the important formulas that will help you in solving the questions along with details of basic concepts. Previous year questions from Sequence and Series topics have also been provided with solutions. Candidates are advised to check the article while preparing this topic for CAT 2021.
Important Formulas for CAT QA Progression and Series
In the below table, the formulas of three different types of progression and series are mentioned.
| Progression & Series | Formulas |
|---|---|
| Arithmetic Progression | Sn = n/2[2a + (n − 1) × d |
| Geometric Progression | Sn=a1−r S n = a 1 − r |
| Harmonic Progression | Harmonic Mean = n /[(1/a) + (1/b)+ (1/c)+(1/d)+….] |
| General Term (nth Term) in Arithmetic Progression | an = a + (n-1)d |
| General Term (nth Term) in Geometric Progression | an = ar(n-1) |
| Calculating nth term from the last term in Arithmetic Progression | an = l – (n-1)d |
| Calculating nth term from the last term in Geometric Progression | an = 1/r(n-1) |
| Sum of first N terms in Arithmetic Progression | sn = n/2(2a + (n-1)d) |
| Sum of first N terms in Geometric Progression | sn = a(1 – rn)/(1 – r) if r < 1 sn = a(rn -1)/(r – 1) if r > 1 |
CAT Quantitative Aptitude: Basic Difference between Sequence and Series
In the below table, the differences between Sequences and Series are given.
| Sequence | Series |
|---|---|
| Sequence is considered as a specific format of the element in some particular order | Series is the total of all the elements of the sequence. |
| The order of all the elements are seen as fixed in sequence | On the other hand, the order of all the elements are not fixed in series. |
| Sequence are represents as 1,2,3,4....n | Series are represents as 1+2+3+4+....n |
| All the order of the elements must be well maintained in sequences | All the order of the elements are not given preferences |
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| How to Prepare for CAT Mensuration? | How to Prepare for CAT Trigonometry? | Shortcut Methods for CAT QA |
CAT Quantitative Aptitude: Basic Concepts of Series
To know the series, one must be aware of the sequences. So, the sequences are the list of some objects that is preceded by a particular pattern whereas series are the sum of an arrangement of terms. It is applicable in different subjects especially in Mathematics.
- Arithmetic Series -
- a, a+d, a+2d, a+3d, a+4d, .......a +(n-1)d
- A1 = a, a2 = a + d, a3 = a + 2d, an = a + (n - 1)d
- Sum of N terms of an Arithmetic Series -
- Sn = n/2 ×(First Term + Last Term)
- Sn = n/2 (2a + (n-1) d)
- Geometric Series -
- a, ar, ar2, ar3, ar4, ar5, ........arn - 1
- a1 = a, a2 = ar, a3 = ar2,
- nth term of the Geometric Series: an = arn - 1
- Sum of N terms of Geometric Series –
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- Harmonic Series –
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Basic Concepts of Sequences in CAT QA
Progressions/ Sequence can be defined as numbers that are arranged in a specific order so that the numbers are able to form a formularised order where the next number can be found. It can be divided in two forms. One is Arithmetic Progression and another one is Geometric Progression.
- Arithmetic Progression is a sequence of numbers. It is found when the difference between any two consecutive terms remains the same. AP defines the next number in the entire series and it is calculated with the process of adding a fixed number i.e called common difference to the previous number in the entire series.
- Geometric Progression is also a sequence of numbers. It is found when the ratio of any two consecutive terms remains the same. In other ways it can be said that the next number in the series is calculated by multiplying a fixed number i.e called common ratio to the previous number in the whole series.
- Harmonic Progression is a sequence of numbers. It is found when the reciprocal of the terms are in Arithmetic Progression. For example, a,b,c,d,e,f are in Harmonic Progression when 1/a, 1/b, 1/c, 1/d, 1/e, 1/f are found in Arithmetic Progression.
CAT Quantitative Aptitude Progression and Series Solved Question
In the section below, some solved questions regarding CAT Progression and Series are given.
Ques: The 2nd term of a Geometric Progression is 1000. The common ratio is r = 1n, n is a natural number. The product of n terms of Geometric Progression is represented by Pn.
If P6 > P5 and P6 > P7, then calculate the sum of all possible values of n?
- 4
- 9
- 5
- 13
Correct Answer: (2)
Ques: If 4 times the 4th term of an Arithmetic Progression is equal to 9 times the 9th term of the Arithmetic Progression then calculate the 13 times the 13th term of the Arithmetic Progression?
- 7 times the 13th term
- 0
- 13 times the 7th term
- 4 times the 4th term + 9 times the 9th term
Correct Answer: (2)
Ques. Which term of the A.P. 3 , 8 , 13 , 18 , . . . is 73 ?
Solution:
3,8,13,18… is given
The first term is, a=3
The common difference is, d=8−3=13−8=...=5
Assume that the nth term is, an=73
Substitute all these values in the general term of an AP:
an=a+(n−1)d
73=3+(n−1)5
73=3+5n−5
73=5n−2
75=5n
15=n
So, 73 is the 15 t h term
Ques. From a list of natural numbers if 25 are taken from the first, then what are the numbers of arithmetic progressions of 6 terms is formed so that the similar difference of the arithmetic progression will be the factor of the sixth term.
- 31
- 32
- 30
- 28
Correct Answer: ( 1)
Ques. A pingpong ball loses its energy of 25% when it touches the ground. What will be the distance in total of the ball before it touches the ground and stops when the height of the drop is meter?
- 210m
- 240m
- 180m
- 200m
Correct Answer: ( 1)
Ques. What is the total of the first 6 terms of the entire series i.e 19683,6561,2187....?
- 29484
- 42168
- 36816
- 42618
Correct Answer: ( 1)
Ques. What is the total of the series 1+2+5+10+17+26+26...till 50 terms.
- 43375
- 40475
- 42250
- None of these
Correct Answer: ( 2)
Ques. What is the subtotal of the first 10 terms of the entire series of 4, 12, 36...
- 39364
- 118096
- 39634
- 177146
Correct Answer: ( 2)
Ques. What will be the ratio of the 10th term of both the arithmetic progression when the ratio of the total till nth term of 2 AP is 6+n/2?
- 24
- 25/2
- 13/2
- 12
Correct Answer: ( 2)
Ques. What is the arithmetic mean of the numbers 842321 and 456661?
- 638817
- 648827
- 648823
- 649491
Correct Answer: ( 4)
Ques. What will be the sum of 8000+6400+5120+4096+...?
- 16000
- 24000
- 30000
- 40000
Correct Answer: ( 4)
Ques. What is the sum of the first 99991 odd numbers?
- 9998200081
- 9998300072
- 9998100090
- 9998200072
Correct Answer: ( 1)
What is the sum of the series 82, 113, 144, ..., 609?
- 5723,5
- 6219
- 5873.5
- 6121
Correct Answer: ( 2)
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CAT Quantitative Aptitude Progression and Series Preparation Tips
In the below section, some preparation tips for CAT Progression and Series are given below.
- Set a time for each section and prepare daily for the basic concepts.
- Note down all the important formulas and practice daily.
- Revise the formulas and apply it in all the sample questions or the question of the previous year.
- Give mock tests daily related to the topic to get more idea about the type of questions that might get asked in the paper.
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*The article might have information for the previous academic years, please refer the official website of the exam.