JEE Main 2025 — Sequences and Series Questions with Solutions

Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms…

In an arithmetic progression, if S₄₀=1030 and S₁₂=57 , then S₃₀-S₁₀ is equal to :

For positive integers n, if 4 an= (n²+5 n+6 ) and Sn=₌₁ⁿ ((1)/(ak) ), then the value of 507 S₂₀₂₅ is :

Consider two sets A and B, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36…

Let Tr be the rth term of an A.P. If for some m, Tm=(1)/(25), ~T₂₅=(1)/(20), and 20 ₌₁²⁵ ~Tr=13, then 5 ~m ₌m² ~m ~Tr i…

If 7=5+(1)/(7)(5+α)+(1)/(7²)(5+2 α)+(1)/(7³)(5+3 α)+… ∞, then the value of α is :

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…

The number of 3 -digit numbers, that are divisible by 2 and 3 , but not divisible by 4 and 9 , is______.

If the sum of the first 10 terms of the series (4.1)/(1+4.1⁴)+(4.2)/(1+4.2⁴)+(4.3)/(1+4.3⁴)+… is (m)/(n), where gcd(m,…

If ₌₁ⁿ Tr=((2 n-1)(2 n+1)(2 n+3)(2 n+5))/(64), then n → ∞ ₌₁ⁿ ((1)/(Tr) ) is equal to :