Sequences and Series – Most Repeated and Important Questions for JEE Mains 2026
Sequences and Series – Most Repeated and Important Questions
JEE MAINS 2026
Q1. The value of
(1 × 2² + 2 × 3² + 3 × 4² + … + 100 × (101)²)
÷
(1² × 2 + 2² × 3 + 3² × 4 + … + 100² × 101)
is equal to:
305/301
306/305
32/31
31/30
Correct Answer: 305/301
Q2. Let the first term a and the common ratio r of a geometric progression be positive integers.
If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to:
241
231
220
210
Correct Answer: 231
Q3. If
1/(√1 + √2) + 1/(√2 + √3) + … + 1/(√99 + √100) = m
and
1/(1·2) + 1/(2·3) + … + 1/(99·100) = n,
then the point (m, n) lies on the line:
11(x − 1) − 100y = 0
11x − 100y = 0
11(x − 1) − 100(y − 2) = 0
11(x − 2) − 100(y − 1) = 0
Correct Answer: 11x − 100y = 0
Q4. If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and
the sum of its eighth, tenth and twelfth terms is 15309, then the sum of its first nine terms is:
757
755
750
760
Correct Answer: 757
Q5. For three positive integers p, q, r,
x^(pq²) = y^(qr) = z^(p²r) and r = pq + 1 such that
3, 3 logᵧ x, 3 log_z y, 7 log_x z are in A.P. with common difference 1/2.
Then r − p − q is equal to:
12
−6
6
2
Correct Answer: 2
Q6. In an arithmetic progression, if S₄₀ = 1030 and S₁₂ = 57, then S₃₀ − S₁₀ is equal to:
525
505
510
515
Correct Answer: 515
Q7. Let 3, 7, 11, 15, …, 403 and 2, 5, 8, 11, …, 404 be two arithmetic progressions.
Then the sum of the common terms in them is equal to:
Correct Answer: 6699
Q8. The sum
1 + (1+3)/2! + (1+3+5)/3! + (1+3+5+7)/4! + … upto infinite terms, is equal to:
3e
2e
4e
6e
Correct Answer: 2e
Q9. If logₑ a, logₑ b, logₑ c are in A.P. and
logₑ a − logₑ 2b, logₑ 2b − logₑ 3c, logₑ 3c − logₑ a are also in A.P.,
then a : b : c is equal to:
6 : 3 : 2
9 : 6 : 4
25 : 10 : 4
16 : 4 : 1
Correct Answer: 9 : 6 : 4
Q10. Consider an A.P. of positive integers, whose sum of the first three terms is 54 and
the sum of the first twenty terms lies between 1600 and 1800.
Then its 11th term is:
108
90
122
84
Correct Answer: 90
Sequences and Series – JEE Mains Theory
This chapter is one of the most scoring chapters in JEE Mains Mathematics. Questions are frequently asked from arithmetic progression, geometric progression, special series and telescoping sums.