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Sequence and Series questions Notes | Study Quantitative Aptitude (Quant) - CAT

Document Description: Sequence and Series questions for CAT 2022 is part of Progressions (Sequences & Series) for Quantitative Aptitude (Quant) preparation. The notes and questions for Sequence and Series questions have been prepared according to the CAT exam syllabus. Information about Sequence and Series questions covers topics like and Sequence and Series questions Example, for CAT 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Sequence and Series questions.

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Question 1: Find the following sum>
1/(22 –1) +1/(42 –1) + 1/(62 –1) + …. +1/(202 –1)
(a) 9/10
(b) 10/11
(c) 19/21
(d) 10/21 

Answer (d)

Sequence and Series questions Notes | Study Quantitative Aptitude (Quant) - CAT

Question 2: Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial salary of Rs. 200 with a rise of Rs. 15 every six months. Assume that the arrangements remained unaltered till December 31, 1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period?
(a) Rs. 93,300
(b) Rs. 93,200
(c) Rs. 93,100
(d) None of these 

Answer (a)

The salary of X in the first year is Rs 300 and then it increases Rs 30 annually.

Hence, the total salary of X is given by: 

X = 12 x (300 + 330 + 360 + 390 + 420 + 450 + 480 + 510 + 540 + 570)

Sequence and Series questions Notes | Study Quantitative Aptitude (Quant) - CAT  [∵ sum of AP]

= 60 x 870 = Rs. 52,200

Similarly, the initial salary of Y was Rs 200 and it increased by Rs 15 every six months. So. the total salary of Y is given by

Y = 6 x [200+215 +230 + 245 +260 ........20 terms]

= 6 x 10 x [2 x 200-19 x 15]    [sumofA.P.]

= 60 x [400 + 285] = Rs. 41.100

Hence, the total salary-paid = 52200 + 41100 = Rs 93300.

Question 3: Let S denote the infinite sum 2 + 5x + 9x2 + 14x3 + 20x4 + …, where   | | < 1, then S equals
(a) {(2-x)/(1-x)3}
(b) {(2-x)/(1+x)3}
(c) {(2+x)/(1-x)3}
(d) {(2+x)/(1+x)3} 

Answer (a)

We will solve this question by using the given options.

In the first option we have,

Sequence and Series questions Notes | Study Quantitative Aptitude (Quant) - CAT

Using the expansion for (1 - x)-3 = 1 + 3x + 6x2 + 10x3 + ..... Sequence and Series questions Notes | Study Quantitative Aptitude (Quant) - CAT

Sequence and Series questions Notes | Study Quantitative Aptitude (Quant) - CAT

= 2 + 5x+9x2 + 14x3 + ....

Which is equal to the given sum. Hence option 1 is the answer.

Question 4: The infinite sum 1 + (4/7) + (9/72) + (16/73) + (25/74) + …. equals
(a) 27/14
(b) 21/13
(c) 49/27
(d) 256/147 

Answer (c)

We have Sequence and Series questions Notes | Study Quantitative Aptitude (Quant) - CAT      .......(1)

Sequence and Series questions Notes | Study Quantitative Aptitude (Quant) - CAT       .......(2)

Subtracting (2) from (1).

Sequence and Series questions Notes | Study Quantitative Aptitude (Quant) - CAT      .......(3)

Multiplying (3) by 1 7, we obtain equation 4:

Sequence and Series questions Notes | Study Quantitative Aptitude (Quant) - CAT     .......(4)

Subtracting (4) from (3).

Sequence and Series questions Notes | Study Quantitative Aptitude (Quant) - CAT

Sequence and Series questions Notes | Study Quantitative Aptitude (Quant) - CAT

Question 5: Consider the set S = (1, 2, 3, …, 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?
(a) 3
(b) 4
(c) 6
(d) 7
(e) 8 

Answer (d)

Let number of terms in the arithmetic progression be n, then

1000 = 1 + (n–1) d

⇒ (n–1) d = 999

⇒ n – 1 = 999/d

Since n is an integer, so n – 1 is also an integer. This means that ‘d’ is a factor of 999.

Now 999 = 33 × 37. so the total factors of 999 are 4 × 2 = 8.

Out of these 8 factors one factor is 999 and we will reject it as in that case there will be only two terms in the

A.P. i.e. 1 and 1000, which is not possible.

Hence, ‘d’ can take 7 different values.

So, in total, 7 A.Ps. are possible.

The document Sequence and Series questions Notes | Study Quantitative Aptitude (Quant) - CAT is a part of the CAT Course Quantitative Aptitude (Quant).
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