COMEDK UGET 2026 Sequence and Series Practice Questions with Solutions

The Sequence and Series chapter holds significant importance in COMEDK UGET 2026 , especially within the Mathematics section, as it directly tests your logical thinking, pattern recognition, and numerical accuracy. When you practise Sequence and Series questions with detailed solutions, you train yourself to quickly identify patterns and apply the correct formula under exam pressure. The most important portions you need to focus on include Arithmetic Progression (AP), Geometric Progression (GP), special series, nth term, sum of n terms, and basic recursive patterns. Occasionally, mixed questions involving number properties or simple algebraic manipulation are also asked, making this chapter both scoring and concept-driven.

In COMEDK UGET, the type and nature of questions from Sequence and Series are usually direct, formula-based, and time-sensitive. You are often asked to find the next term, missing term, nth term, or sum of a series, with calculations designed to be short but precise. Analysis of previous years’ papers shows that AP-based questions dominate, followed by GP questions involving ratios and exponential growth. In some years, questions on odd-even term patterns, alternating series, and simple series like squares, cubes, or mixed number sequences were also included. The difficulty level has generally remained easy to moderate, but careless calculation errors can cost you marks if your basics are not strong.

To prepare effectively for this chapter, you should begin by mastering core formulas for AP and GP and understanding how they are derived, rather than memorising them blindly. While practising Sequence and Series questions with solutions, you should focus on speed improvement and pattern identification, as COMEDK questions reward quick recognition over lengthy calculations. Solve previous year questions to understand recurring patterns, then move on to mixed practice sets to build confidence. Make it a habit to analyse your mistakes after every practice session—this helps you avoid repeating errors and ensures that Sequence and Series becomes one of your most reliable scoring areas in COMEDK UGET 2026.

Also Check - Do or Die Chapters for COMEDK UGET 2026 Mathematics

COMEDK UGET 2026 Sequence and Series Important Topics

Sequence and Series is a part of the Algebra section in COMEDK UGET 2026 Mathematics syllabus . In the following table, we have provided all the subtopics included in Sequence and Series chapter. COMEDK Sequence and Series sample questions are prepared based on the same topics, so you must prepare them well before solving the practice papers.

COMEDK UGET 2026 Sequence and Series Expected Weightage

As per the past years' question paper trends, you can expect around 10 questions from the COMEDK Sequence and Series chapter. This means, Sequence and Series in COMEDK UGET question paper 2026 will have an approximate weightage of 20%. In the following table, we have listed the expected weightage for COMEDK UGET 2026 Sequence and Series:

COMEDK UGET 2026 Sequence and Series Practice Questions with Solutions

After analyzing the recent question paper trends, our experts have curated some sample questions from the Sequence and Series chapter. You are advised to practice these questions thoroughly while doing your preparation/ revision. You can check COMEDK UGET 2026 Sequence and Series practice questions with solutions below:

Q1. Consider an infinite geometric series with first term a and common ratio r. If the sum of an infinite geometric series is 4 and the second term is 3/4 then:

a. a = 1, r = -3/4

b. a = 3, r = 1/4

c. a = -3, r = -1/4

d. a = -1, r = 3/4

Ans. b. a = 3, r = 1/4

Solution: To determine the correct values for a and r, we need to use the properties of infinite geometric series.

The sum of an infinite geometric series can be expressed as:

S = a/1-r

We are given that the sum of the infinite series is 4

a/1-r = 4 …1

The second term of the series can be calculated as

ar

We are given that the second term is 3/4

ar = 3/4 …2

From equation (2), we can express a in terms of r

a = 3/4r

Substitute this into equation (1):

(3/4r)/1-r = 4

Simplify and solve for r:

3/4r(1-r) = 4

3 = 16r(1-r)

3 = 16r - 16r ²

16r ² - 16r + 3 = 0

Solving this quadratic equation for r,

r = -b±√(b ² - 4ac)/2a

here , a = 16, b = -16, and c = 3

Solving the quadratic equation,

r = 3/4 or r = 1/4

Now, using these values for r, we find corresponding a

For r = 3/4

a =3/4(3/4) = 1

Similarly, for r = 1/4, a = 3

The correct pairs of values are:

a = 1, r = 3/4

a = 3, 4 = 1/4

Q2. The sum of four numbers in a geometric progression is 60, and the arithmetic mean of the first and the last number is 18. Then the numbers are

a. 10, 8, 16, 26

b. 32, 16, 4, 8

c. 32, 16, 8, 2

d. 4, 8, 16, 32

Ans. d. 4, 8, 16, 32

Solution: Let's consider four numbers in a geometric progression. We can denote them as follows:

a, ar, ar ² , ar ³ …

Where a is the first term and r is the common ratio

We are given two conditions:

The sum of the four numbers is 60:

a + ar + ar ² + ar ³ = a(1 + r + r ² + r ³ ) = 60

The arithmetic mean of the first and the last number is 18:

a + ar3/2 = 18 = a(1+r ³ ) = 36

Now, let’s check the options provided.

Option D is: 4, 8, 16, 32.

Verify if these are in a geometric progression:

Here, a = 4.

The ratio from 4 to 8 is 8/4 = 2, from 8 to 16 is 16/8 = 2, and from 16 to 32 is 32/16=2, thus, r = 2.

Check the sum

4 + 8 + 16 + 32 = 60

Check the arithmetic mean of the first and last number:

4+32/2 = 36/2 = 18

Since both conditions are satisfied by Option D, the numbers in the geometric progression are:

4, 8, 16, 32.

Q3. If the 6th term of G.P is -1/32 and 9th term is 1/256 the r is?

a. 2

b. -1/2

c. 1/2

d. -2

Ans. b. -1/2

Solution: Let's solve the problem step by step.

The general term of a geometric progression (GP) is given by:

Tn = ar ^n-1

where:

a is the first term,

r is the common ratio.

According to the problem:

The 6th term is:

T ₆ = a r ⁵ = -1/32

And the 9th term is:

T ₉ = a r ⁸ = 1/256

To eliminate a, divide 9th term by 6th term,

T ₉ /T ₆ = a r ⁸ /a r ⁵ = (1/256)/(-1/32)

Simplify the right side:

r ³ = 1/256 x (-32/1) = -1/8

Now solve for r,

r ³ = -1/8 = r = -1/2

Q4. If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of an AP is?

a. 1700

b. 1650

c. 3300

d. 3500

Ans. b. 1650

Solution: Here, T ₁₂ = a + 11d and T ₂₂ = a + 21d

Since, 100 = T ₁₂ + T ₂₂
100 = a + 11d + a + 21 d

a + 16d = 50 …1

Now, S33 = 33/2[2a + (33 - 1)d]

33(a+16d)

From equation 1

33 x 50 = 1650

Q5. If three numbers a, b, c constitute both an A.P and G.P, then

a. a = b = c

b. a = b + c

c. ab = c

d. a = b - c

Ans. a. a = b = c

Solution: To solve this, let's first understand what it means for numbers to form an arithmetic progression (A.P) and a geometric progression (G.P).

Arithmetic Progression (A.P): A sequence of numbers is said to be in arithmetic progression when the difference between any two successive members is a constant. For example, in the sequence a, b, c, where b, c are successive terms after a, they must satisfy:

b - a = c - b

Simplifying, we get:

2b = a + c

Geometric Progression (G.P): A sequence is in geometric progression when each term after the first is multiplied by a constant called the common ratio. In the sequence a, b, c, they must satisfy: b/a = c/b

If a, b, and c are non zero, we can rearrange the equation as,

b ² = ac

Now, we know that a, b, c are in AP and GP. The key to solving this is to see what happens when we apply the conditions of both progressions. From the G.P. condition, b ² = ac. From the A.P. condition, 2b = a + c if we substitute a + c = 2b into GP equation,

b ² = ac

b ² = a (2b - a)

Let’s simplify this:

b ² = 2ab - a ²

This actually is a quadratic equation in terms of a,

a ² - 2ab + b ² = 0

which simplifies to:

(a - b) ² = 0

Thus, a - b = 0

a = b

If a = b, then substituting this back in a + c = 2b

a + c = 2b

c = a

Thus, a = b = c, which concludes that all three numbers must be equal in both A.P. and G.P. when they are non-zero and effective.

Important Portions of Sequence and Series & Study Strategy

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Previous Year COMEDK Question from Sequence and Series

Check the type of questions asked in COMEDK exam from this chapter.

Revision Strategy for Sequence & Series Chapter

You can focus on this strategy to successfully attempt questions.

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