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🚀 COMPLETE PREPARATION LOOP: LEARN → PRACTICE → ANALYZE

Sequences & Series Preparation Hub

Master Sequences & Series with coaching-grade theory notes, verified video lectures, and 10 interactive MCQs with instant mistake analysis. Continue with 500+ adaptive questions inside the Exam Sprinter app.

📘 Theory Notes ✍️ Interactive Practice ⏱️ CBT Simulator

What is Sequences & Series?

Sequences & Series covers the essential principles and concepts required for JEE Main.

💡 Why Study Sequences & Series?

Highly important, frequently tested in JEE Main.

Parameter	Details / Relevance
Target Exam	JEE Main
Subject Category	Mathematics
Estimated Study Duration	10 Hours
Expected Questions	2 Questions
Difficulty Index	Easy
Interactive Solved MCQs	10 Questions with AI Diagnostics
Adaptive App Practice	500+ Questions & Real-Time AI Tutor

⚠️ Common Pitfalls to Avoid

Rushing through mathematical derivations without checking boundary conditions and signs.
Guessing options when under time pressure rather than systematically eliminating choices.
Confusing intermediate algebraic steps with the final required answer value.

✓ COACHING-GRADE CLASSROOM NOTES

Sequences & Series Theory & Derivations

Browse All Notes Library ›

Access comprehensive classroom-grade derivations and NCERT micro-extracts for Sequences & Series. Features step-by-step proofs and standard assumptions.

Important Formulas & Cheat Sheet

AP: $$S_n = \frac{n}{2}(2a + (n-1)d)$$
GP: $$S_n = \frac{a(r^n - 1)}{r-1}$$
$$\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$$

✍️ STEP 3: PRACTICE & ANALYZE

Sequences & Series Interactive Practice

⏱️ Take Chapter CBT Test

Solve these 10 standard exam-level questions. The system tracks your response time, detects rapid guessing via Cognitive Reading Thresholds, and outputs your post-session diagnosis.

Interactive Practice Progress:0 / 10 Answered

⏱️ Launch Chapter CBT Simulator

Q1Arithmetic & Geometric Progressions

Expected: 60sEasy

If the sum of first 11 terms of an A.P., a1, a2, a3, .... is 0 (a $\ne$ 0), then the sum of the A.P., a1 , a3 , a5 ,....., a23 is ka1 , where k is equal to :

Q2Arithmetico-Geometric Progression

Expected: 60sEasy

If a1, a2, a3, ............... an are in A.P. and a1 + a4 + a7 + ........... + a16 = 114, then a1 + a6 + a11 + a16 is equal to :

Q3Special Series Summation

Expected: 60sEasy

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,........,is

Q4Arithmetic & Geometric Progressions

Expected: 60sEasy

If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

Q5Arithmetico-Geometric Progression

Expected: 90sMedium

The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is :

Q6Special Series Summation

Expected: 90sMedium

The sum 1 + 2 . 3 + 3 . 32 + ......... + 10 . 39 is equal to :

Q7Arithmetic & Geometric Progressions

Expected: 90sMedium

If $A = \sum\limits_{n = 1}^\infty {{1 \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}}$ and $B = \sum\limits_{n = 1}^\infty {{{{{( - 1)}^n}} \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}}$ , then ${A \over B}$ is equal to :

Q8Arithmetico-Geometric Progression

Expected: 90sMedium

Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{10}=390$ and the ratio of the tenth and the fifth terms is $15: 7$ , then $\mathrm{S}_{15}-\mathrm{S}_5$ is equal to :

Q9Special Series Summation

Expected: 120sHard

The number of integral solutions $x$ of $\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^{2} \geq 0$ is :

Q10Arithmetic & Geometric Progressions

Expected: 120sHard

The sum $\sum\limits_{n = 1}^\infty {{{2{n^2} + 3n + 4} \over {(2n)!}}}$ is equal to :

🗺️ Recommended Learning Sequence

Permutations & Combinations➔Sequences & Series (Current)➔Limits, Continuity & Differentiability

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Sequences & Series Preparation Hub

What is Sequences & Series?

💡 Why Study Sequences & Series?

⚠️ Common Pitfalls to Avoid

Sequences & Series Theory & Derivations

Important Formulas & Cheat Sheet

Sequences & Series Interactive Practice

If the sum of first 11 terms of an A.P., a1, a2, a3, .... is 0 (a ≠ \ne = 0), then the sum of the A.P., a1 , a3 , a5 ,....., a23 is ka1 , where k is equal to :

If a1, a2, a3, ............... an are in A.P. and a1 + a4 + a7 + ........... + a16 = 114, then a1 + a6 + a11 + a16 is equal to :

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,........,is

If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is :

The sum 1 + 2 . 3 + 3 . 32 + ......... + 10 . 39 is equal to :

Let SnS_nSn​ denote the sum of the first nnn terms of an arithmetic progression. If S10=390S_{10}=390S10​=390 and the ratio of the tenth and the fifth terms is 15:715: 715:7, then S15−S5\mathrm{S}_{15}-\mathrm{S}_5S15​−S5​ is equal to :

The number of integral solutions xxx of log⁡(x+72)(x−72x−3)2≥0\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^{2} \geq 0log(x+27​)​(2x−3x−7​)2≥0 is :

The sum ∑n=1∞2n2+3n+4(2n)!\sum\limits_{n = 1}^\infty {{{2{n^2} + 3n + 4} \over {(2n)!}}} n=1∑∞​(2n)!2n2+3n+4​ is equal to :

🗺️ Recommended Learning Sequence

Ready to achieve complete mastery in Sequences & Series?

If the sum of first 11 terms of an A.P., a1, a2, a3, .... is 0 (a $\ne$ 0), then the sum of the A.P., a1 , a3 , a5 ,....., a23 is ka1 , where k is equal to :

Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{10}=390$ and the ratio of the tenth and the fifth terms is $15: 7$ , then $\mathrm{S}_{15}-\mathrm{S}_5$ is equal to :

The number of integral solutions $x$ of $\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^{2} \geq 0$ is :

The sum $\sum\limits_{n = 1}^\infty {{{2{n^2} + 3n + 4} \over {(2n)!}}}$ is equal to :