CAT Sequences & series Questions

A sequence is an ordered list of terms; a series is their sum. Questions may use arithmetic or geometric progressions, recurring patterns or telescoping sums.

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Key concepts

• Common difference and common ratio
• The nth term and partial sums
• Telescoping and recurring patterns

CAT sequences & series practice questions

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Common mistakes

• Confusing a term with the sum of terms.
• Applying an infinite geometric sum when the common ratio has magnitude at least one.

Practical solving approaches

• Write the first few terms and identify the rule precisely.
• Check the starting index and number of terms before applying a sum formula.

Sequences & series FAQs

When does an infinite geometric series have a finite sum?

It converges when the absolute value of the common ratio is less than one. Its sum is the first term divided by one minus the ratio.

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CAT Sequences & series Questions

A sequence is an ordered list of terms; a series is their sum. Questions may use arithmetic or geometric progressions, recurring patterns or telescoping sums.

13 free practice questions

Key concepts

• Common difference and common ratio
• The nth term and partial sums
• Telescoping and recurring patterns

CAT sequences & series practice questions

Question 1Multiple choiceMEDIUM

Question 1

How many men were working on the fifth day ?

Refer to the data below and answer the questions that follow.

A group of men was employed to shift 545 crates. Everyday after the first, 6 more men than that on the previous day were put on the job. Also, everyday after the first, each employed man, shifted 5 fewer crates than the number of crates moved by each man on the previous day. All workers shift an equal number of crates on any given day. It took five days to finish the work.

Choose an answer

A.13 B.25 C.19 D.75

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Question 2Type in the answerMEDIUM

Question 2

Type in your answer in the input box provided below the question.

Answer the questions independently of each other.

In an archery contest, there are x targets. For y = 1, 2, ...., x, there are 2x - y archers who miss yth target. If the total numbers of targets missed is 4095, then what is the value of x?

Your answer

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Question 3Multiple choiceEASY

Question 3

Select the correct alternative from the given choices.

Answer the questions independently of each other.

The value of the series 1! + 2.2! + 3.3! + ...... (upto n terms) is:

Choose an answer

A.

B.

C.

D.

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Question 4Multiple choiceMEDIUM

Question 4

Select the correct alternative from the given choices.

Answer the questions independently of each other.

An insect starts from a point and travels in a straight path of length equal to 1 mm in the first second, half of that distance in the next second and so on. In how much time would it reach a point 3 mm away from its starting point?

Choose an answer

A.8 secB.9 secC.12.5 secD.The insect would never reach a point 3 mm away from the starting point.

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Question 5Multiple choiceMEDIUM

Question 5

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Choose an answer

A.410 hoursB.450 hoursC.475 hoursD.525 hours

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Question 6Multiple choiceMEDIUM

Question 6

Select the correct alternative from the given choices.

Answer the questions independently of each other.

The first term of two A.P.s is 5. What is the ratio of their fourth terms, if the common difference of the first A.P. is square of that of the second A.P. and vice versa?

Choose an answer

A.1 : 1B.1 : 2C.2 : 5D.None of these

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Question 7Multiple choiceMEDIUM

Question 7

Select the correct alternative from the given choices.

Answer the following questions based on the information given below.

The number of common terms in the two sequences 17, 21, 25, … , 417 and 16, 21, 26, … , 466  is.

Choose an answer

A.78B.19C.20 D.77E.22

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Question 8Multiple choiceMEDIUM

Question 8

Select the correct alternative from the given choices.

Answer the questions independently of each other.

In a "Strong Man" competition a contestant is supposed to roll a stone weighing a ton across some distance. The bulky contestant in his first great effort pushes the stone upto half the finishing distance. However due to the mass of the stone and the physical impossibility of the task, the stone rolls back half the distance it covered. Undeterred, the contestant heaves the stone upto half of what he had pushed it earlier. This time too, the stone rolls back half of what it covered in the throw. The contestant tries again, pushes the stone to half the distance he had pushed in the earlier attempt and the stone similarly rolls back. Finally, after 10 such attempts the contestant gives up, though on the last occassion he manages to hold the stone from rolling back. What would be the ratio of the distance that he made the stone to cover in his 10 attempts to that he would have made it cover, had he continued his attempts forever?

Choose an answer

A.1 : 1B.2 : 1C.4 : 1D.Cannot be determined

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Question 9Multiple choiceMEDIUM

Question 9

Select the correct alternative from the given choices

Choose an answer

A.5B.6C.3D.None of the Above

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Question 10Multiple choiceMEDIUM

Question 10

Select the correct alternative from the given choices

Choose an answer

A.2nd dayB.3rd dayC.4th dayD.5th day

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Question 11Multiple choiceHARD

Question 11

Select the correct alternative from the given choices

A total of ‘x’ workers start working on a project on the first day. On the second, fourth, sixth and eighth days, half of the workers
working on the project the previous day left the project, while on the third, fifth and seventh days, one-third of the workers
working on the project the previous day left the project. The project was completed in 8 days. If only one employee worked on the
project for 8 days, what is the value of ‘x’?

Choose an answer

A.45B.36C.60D.54

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Question 12Type in the answerMEDIUM

Question 12

Enter your response (as an integer) using the virtual keyboard in the box provided

The fourth term of a geometric progression with the common ratio is the same as the first term is 6561. If all the terms of the progression are positive, find the remainder when the sum of the first eight terms is divided by 6.

Your answer

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Question 13Type in the answerMEDIUM

Question 13

Enter your response (as an integer) using the virtual keyboard in the box provided

Your answer

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Common mistakes

• Confusing a term with the sum of terms.
• Applying an infinite geometric sum when the common ratio has magnitude at least one.

Practical solving approaches

• Write the first few terms and identify the rule precisely.
• Check the starting index and number of terms before applying a sum formula.

Sequences & series FAQs

When does an infinite geometric series have a finite sum?

It converges when the absolute value of the common ratio is less than one. Its sum is the first term divided by one minus the ratio.

More Algebra practice

• Functions & graphs →
• Inequalities & modulus →
• Linear equations & word problems →
• Logarithms, indices & surds →
• Polynomials, higher-degree equations & binomial expansion →
• Quadratic equations & expressions →