Last Updated: May 2026
IPMAT Sequences and Series 2027 is one of the highest-yield Quantitative Ability topics in the IIM Indore IPMAT, IPMAT Rohtak, and JIPMAT papers. Last 5 years’ analysis shows 5-7 questions per IPMAT paper from sequences and series — making it the single biggest scoring topic in QA. This guide covers AP, GP, HP, AGP, special series, summation tricks, and 30 practice MCQs.
Quick Facts: IPMAT Sequences & Series 2027
| Aspect | Detail |
|---|---|
| Average IPMAT questions/year | 5-7 (combined MCQ + SA) |
| Difficulty | Easy to Moderate |
| Most-tested zones | Sum of n terms, AP-GP relations, AGP, special series |
| Trap zone | HM-GM-AM inequality (HM ≤ GM ≤ AM) |
Arithmetic Progression (AP) — Master Formulae
- n-th term: an = a + (n−1)d
- Sum of n terms: Sn = (n/2)[2a + (n−1)d] = (n/2)(a + l), where l is the last term
- If a, b, c are in AP → 2b = a + c (Arithmetic Mean property)
- Sum of first n natural numbers: 1 + 2 + … + n = n(n+1)/2
Geometric Progression (GP) — Master Formulae
- n-th term: an = arn−1
- Sum of n terms (r ≠ 1): Sn = a(rn − 1)/(r − 1)
- Sum to infinity (|r| < 1): S∞ = a/(1 − r)
- If a, b, c are in GP → b² = ac (Geometric Mean property)
Harmonic Progression (HP)
- If a, b, c are in HP → 1/a, 1/b, 1/c are in AP.
- HM of two numbers = 2ab/(a+b).
- HM ≤ GM ≤ AM for positive numbers; equality iff all are equal.
Arithmetic-Geometric Progression (AGP) — IPMAT Favourite
AGP: a, (a+d)r, (a+2d)r², …
- Sum of n terms: Sn = a/(1−r) + dr(1−rn−1)/(1−r)² − [a + (n−1)d]·rn/(1−r) — derived via S − rS technique.
- Sum to infinity (|r|<1): S∞ = a/(1−r) + dr/(1−r)²
Special Series — High-Yield Identities
| Series | Sum |
|---|---|
| 1 + 2 + 3 + … + n | n(n+1)/2 |
| 1² + 2² + 3² + … + n² | n(n+1)(2n+1)/6 |
| 1³ + 2³ + 3³ + … + n³ | [n(n+1)/2]² |
| 1·2 + 2·3 + 3·4 + … + n(n+1) | n(n+1)(n+2)/3 |
| 1·2·3 + 2·3·4 + … + n(n+1)(n+2) | n(n+1)(n+2)(n+3)/4 |
AP-GP Relations & Means
- If A, G, H are AM, GM, HM of two positive numbers a, b: A·H = G²; A > G > H.
- n AMs between a and b: d = (b−a)/(n+1)
- n GMs between a and b: r = (b/a)1/(n+1)
Sum of Telescoping Series
For series like 1/(1·2) + 1/(2·3) + 1/(3·4) + … use partial fractions:
1/(k(k+1)) = 1/k − 1/(k+1) → sum telescopes to 1 − 1/(n+1) = n/(n+1).
Common IPMAT Question Types
- Find the sum to infinity of an AGP/GP — direct formula.
- Insert n means between two numbers — d or r calculation.
- Apply AM-GM-HM inequality to optimize/find min-max.
- Sum of squares/cubes — apply special series identities.
- Find missing term given partial AP/GP info.
5 Solved Examples
Example 1 (IPMAT 2024)
Find the sum: 1 + 11 + 111 + … + (n digits of 1).
Solution: Each term k = (10k−1)/9. Sum = (1/9) × [Σ10k − n] = (1/9) × [(10n+1−10)/9 − n] = (10n+1−9n−10)/81.
Example 2
If 8th term of an AP is 17 and 12th term is 25, find the 18th term.
Solution: a + 7d = 17, a + 11d = 25 → d = 2, a = 3. a18 = 3 + 17·2 = 37.
Example 3
Sum to infinity of 1 + 2x + 3x² + 4x³ + … where |x|<1.
Solution: AGP with a=1, d=1, r=x. Sum = 1/(1−x)² .
Example 4
If a, b, c are in HP, prove (a+b)/(2a−b) + (b+c)/(2c−b) ≥ 4.
Solution: Use 1/a, 1/b, 1/c in AP and AM-HM.
Example 5
How many three-digit numbers between 100 and 999 are divisible by 7?
Solution: First = 105, Last = 994; n = (994−105)/7 + 1 = 128.
FAQ — IPMAT Sequences & Series 2027
Q1. Which is more frequent on IPMAT — AP or GP?
Q2. What is the AM-GM-HM inequality?
Q3. How do I sum an AGP quickly?
Q4. What is the sum of the first n cubes?
Q5. Are calculators allowed in IPMAT 2027?
Practice MCQs
[cg_quiz id=”ipmat-sequences-series-2027″]
Related Reading
- IPMAT Algebra 2027
- IPMAT Number System 2027
- IPMAT Data Interpretation 2027
- IPMAT Verbal Ability 2027
- Free IPMAT Mock Test
Bottom line: Sequences & Series can fetch you 6 marks per IPMAT paper if you nail the 5 special series identities, AGP, and AM-GM inequality. This single chapter is worth 30+ days of focused practice.