Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20252 AprilMorning Shift
Exam
JEE Main
Year
2025
Date
2 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Sequences and Series

JEE Main 2025 · 2 April · Morning Shift · Mathematics · Sequences and Series

Let a_1, a_2, a_3 be in an A.P. such that ∑_ k=1 ^ 12 a_ 2 k-1...

Let a1,a2,a3…a_1, a_2, a_3 \ldots be in an A.P. such that ∑k=112a2k−1=−725a1,a1≠0\sum_{\mathrm{k}=1}^{12} \mathrm{a}_{2 \mathrm{k}-1}=-\frac{72}{5} \mathrm{a}_1, \mathrm{a}_1 \neq 0. If ∑k=1nak=0\sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{a}_{\mathrm{k}}=0, then n is:

Options

  1. A11
  2. B10
  3. C18
  4. D17

Correct answer

A. 11

Step-by-step solution

Let a1=aa_1=a, common difference =d=d
a1+a3+a5+……+a23=−725aa_1+a_3+a_5+\ldots \ldots+a_{23}=-\frac{72}{5} a
122[2a+11×2d]=−725a\frac{12}{2}[2 a+11 \times 2 d]=-\frac{72}{5} a
12a+132d=−725a12 a+132 d=-\frac{72}{5} a
132a+132×5d=0132 a+132 \times 5 d=0
a=−5 d\mathrm{a}=-5 \mathrm{~d}
n2(2a+(n−1)d)=0⇒−10 d+nd−d=0\frac{\mathrm{n}}{2}(2 \mathrm{a}+(\mathrm{n}-1) \mathrm{d})=0 \Rightarrow-10 \mathrm{~d}+\mathrm{nd}-\mathrm{d}=0
n=11\mathrm{n}=11
Practice Sequences and Series on Quantrex Academy →

More from Sequences and Series

Let α = 3+4+8+9+13+14+… upto 40 terms. If ( β)^ (α)/(1020) is a root of the equation… JEE Main 2026The sum 1 + (1)/(2)(1^2 + 2^2) + (1)/(3)(1^2 + 2^2 + 3^2) + … upto 10 terms is equal to : JEE Main 2026The value of 1^3 - 2^3 + 3^3 - … + 15^3 is: JEE Main 2026The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a… JEE Main 2026For the functions f(θ) = α ^2θ + β ^2θ , and g(θ) = α ^2θ + β ^2θ , α > β > 0 , let _ 0 <… JEE Main 2026If the sum of the first 10 terms of the series (1)/(1 + 1^4 × 4) + (2)/(1 + 2^4 × 4) +… JEE Main 2026Let A_1, A_2, A_3, …, A_ 39 be 39 arithmetic means between the numbers 59 and 159 . Then… JEE Main 2026Let the sum of the first n terms of an A.P. be 3n^2 + 5n . Then the sum of squares of the… JEE Main 2026∑_ n=1 ^ 10 ( (528)/(n(n+1)(n+2)) ) is equal to: JEE Main 2026Let α=(1)/(4)+(1)/(8)+(1)/(16)+…∞ and β=(1)/(3)+(1)/(9)+(1)/(27)+…∞ . Then the value of… JEE Main 2026The first term of an A.P. of 30 non-negative terms is (10)/(3) . If the sum of this A.P.… JEE Main 2026Let a_1, a_2, a_3, … be an A.P. and g_1 = a_1, g_2, g_3, … be an increasing G.P. If a_1 =… JEE Main 2026The sum (1^3)/(1) + (1^3 + 2^3)/(1 + 3) + (1^3 + 2^3 + 3^3)/(1 + 3 + 5) + ⋯ up to 8… JEE Main 2026Let α, α + 2, α ∈ ℤ , be the roots of the quadratic equation x(x+2) + (x+1)(x+3) +… JEE Main 2026Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common… JEE Main 2026If ∑_ k=1 ^ n a_k = 6n^3 , then ∑_ k=1 ^ 6 ( a_ k+1 - a_k 36 )^2 is equal to _______. JEE Main 2026 Full Sequences and Series list Sequences and Series JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs