Important JEE Main 2026 Questions on Sequences, Series, and Binomial Theorem with Solutions

The Sequences, Series and Binomial Theorem chapters are an important part of the JEE Main 2026 Math syllabus. To get a good score in the Mathematics section, you need to revise the important formulae like the sum of n-terms of an AP/GP, the general term of GP, binomial expansions, etc. Start your JEE Main 2026 preparation by clearing your basics. We have provided some important solved questions on Sequence, Series and Binomial Theorem for JEE Main 2026. Solving these questions can boost your preparation level. Take a look at the JEE Main 2026 questions and the solutions provided in this article.

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JEE Main 2026 Sequence, Series and Binomial Theorem Practice Questions

Check out some of the best solved questions on Sequence, Series and Binomial Theorem for JEE Main 2026:

Q1. The first term of an AP is 5, the 10th term is 32. Find the sum of the first 20 terms.

Solution

First term a = 5. 10th term = a+(10−1)d = 32 ⇒ 5 + 9d = 32 ⇒ d = 3. So the sum of first 20 terms:

S20 = 20/ 2 [2a + (20 - 1)d] = 10[2 X 5 + 19 X 3] = 10[10 + 57] = 10 X 67 = 670

Answer: 670

Q2. In a GP the third term is 24 and the sixth term is 192. Find the common ratio r and the first term, then the sum of the first 8 terms.

Solution

Let the first term = a, ratio = r. Then third term = ar2 = 24. Sixth term = ar5 = 192. Divide the second by the first:

ar5 / ar2 = r3 = 192 / 24 = 8 ⇒ r3 = 8 ⇒ r = 2

Then a22 = 24 ⇒ a = 24/ 4 = 6. Sum of first 8 terms:

S8 = a r8 - 1/ r - 1 = 6 28 - 1/ 2 - 1 = 6(256 - 1) = 6 X 255 = 1530

Answer: 1530

Q3. In the expansion of (2x + 3)8, find the coefficient of x5.

Solution

General term: Tr+1 = (8 r​)(2x)8-r(3)r. For x5, the power of x is from (2x)8-r so 8-r = 5 ⇒ r = 3.

Then coefficient = (8 3) X 25 X 33 = 56 X 32 X 27 = 56 X 864 = 48384.

Answer: x5 = 48384

JEE Main 2026 Sequence, Series and Binomial Theorem Sample Questions PDF

To get the complete list of solved JEE Main sample papers on Sequence, Series and Binomial Theorem chapters, click on the PDF below:

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Preparation Tips for JEE Main 2026 Sequence, Series and Binomial Theorem

Sequences, Series and Binomial Theorem are a part of the JEE Main 2026 Mathematics section. Find below some of the JEE Main 2026 preparation tips to ace the Mathematics section:

• Daily practice: Solve 2 to 3 problems from each of the Mathematics topics.

• Formula sheet: Try to maintain a one-page sheet listing key series/ sequence sums and binomial identities and do not forget to review it every week.

• Timed practice: Since JEE Main demands speed, practice each problem under timed situations (10 minutes maximum for each question).

• Error log: You can maintain a log of mistakes, such as the misapplication of the sum formula, and review it weekly.

• Mock revision: Include a full test set of 10 to 12 sequence/series/binomial questions in each session of your JEE Main 2026 mock test , to develop accuracy.

• Clear basics: If you struggle with common ratios or differences, or simple coefficients, revisit the study materials and clear the fundamentals first.

The practice questions provided here are some of the important questions for JEE Main 2026 from the Sequence, Series and Binomial Theorem chapters. The candidates can improve their preparation level by solving more and more sets of JEE Main Mathematics practice questions .

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