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JEE Sequences and Series PYQs with Solutions

38 previous year questions from Sequences and Series (JEE Main & Advanced IOQM) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

38 questionsIOQMAnswers + solutions

About Sequences and Series PYQs

Sequences and Series has 38 previous year questions in the Quantrex Academy JEE Main & Advanced IOQM bank. The 38 questions in this list come from Olympiad workbook (38). Each question opens on its own page with the options, the correct answer and the worked solution where available.

JEE Sequences and Series PYQs with Solutions

About Sequences and Series PYQs

Sequences and Series questions with solutions

A finite set M of positive integers consists of distinct perfect squares and the number 92 . The average of the numbers in M is 85 . If we remove 92 from M , the average drops to

If ∑_ k=1 ^N (2 k+1)/((k^2+k)^2)=0.9999 then determine the value of N .

A group of women working together at the same rate can build a wall in 45 hours. When the work started, all the women did not start working together. They joined the work over a

Let m be the smallest positive integer such that m^2+(m+1)^2+…+(m+10)^2 is the square of a positive integer n . Find m+n .

Let u, v, w be real numbers in geometric progression such that u>v>w . Suppose u^ 40 =v^ n =w^ 60 . Find the value of n .

The sequence a_n _ n ≥ 0 is defined by a_0=1, a_1=-4 and a_ n+2 =-4 a_ n+1 -7 a_n , for n ≥ 0 . Find the number of positive integer divisors of a_ 50 ^2-a_ 49 a_ 51 .

Let the sum ∑_ n=1 ^9 (1)/(n(n+1)(n+2)) written in its lowest terms be (p)/(q) . Find the value of q-p .

Consider the set T of all triangles whose sides are distinct prime numbers which are also in arithmetic progression. Let Δ ∈ T be the triangle with the least perimeter. If a^ ∘ is

Starting with a positive integer M written on the board, Alice plays the following game: in each move, if x is the number on the board, she replaces it with 3 x+2 . Similarly

∑_ k=1 ^ 40 ( 1+(1)/(k^2)+(1)/((k+1)^2) )=a+(b)/(c) where a, b, c ∈ ℕ, b < c, gcd(b, c)=1 , then what is the value of a+b ?

Integers 1,2,3 … … . n where n>2 , are written on a board. Two numbers m, k such that 1 < m < n .1 < k < n are removed and the average of the remaining numbers is found to be 17 .

Five distinct 2-digit numbers are in a geometric progression. Find the middle term.

Suppose x is a positive real number such that \ x\ .[x] and x are in the geometric progression. Find the least positive integer n such that x^n>100 . (Here [x] denotes the integer

Each of the numbers x_1, x_2, … … … . x_ 101 is ± 1 . What is the smallest positive value of ∑_ 1 ≤ i ≤ j ≤ 101 x_i x_j ?

A natural number k>1 is called good if there exist natural numbers a_1 < a_2 < … … … < a_k such that 1 a_1 + 1 a_2 +… …+ 1 a_k =1 Let f(n) be the sum of the first n good numbers

A natural number n is said to be good if n is the sum of r consecutive positive integers, for some r ≥ 2 . Find the number of good numbers in the set \ 1,2, … …, 100) .

Let a_1=24 and form the sequence a_n, n ≥ 2 by a_n=100 a_ n-1 +134 . The first few terms are 24,2534,253534,25353534, … … … What is the least value of n for which a_ n is

What is the largest positive integer n such that (a^2)/((b)/(29)+(c)/(31))+(b^2)/((c)/(29)+(a)/(31))+(c^2)/((a)/(29)+(b)/(31)) ≥ n(a+b+c) holds for all positive real numbers a,b,c.

What is the value of ∑_ 1 ≤ i < j ≤ 10 i+j= odd (i+j)-∑_ 1 ≤ i < j ≤ 10 i+j= even (i+j) ?