JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(a_1, a_2, \ldots, a_{2024}\) be an Arithmetic Progression such that \(a_1+\left(a_5+a_{10}+a_{15}+\ldots+a_{2020}\right)+a_{2024}=2233\). Then \(a_1+a_2+a_3+\ldots+a_{2024}\) is equal to _______
- A 11132
- B 11134
- C 11136
- D 11138
Answer & Solution
Correct Answer
(A) 11132
Step-by-step Solution
Detailed explanation
As \(a_1+a_5+a_{10}+\ldots+a_{2020}+a_{2024}=2233\) ...(1) We know in arithmetic progression. Sum of terms equidistant from ends is equal \(\therefore\) from (1) \(\underbrace{a_1+a_{2024}=a_5+a_{2020}=a_{10}+a_{2015}=\ldots}_{203 \text { pairs }}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The value of \(\lim _{x \rightarrow 0}\left(\frac{x}{\sqrt[8]{1-\sin x}-\sqrt[8]{1+\sin x}}\right)\) is equal to:JEE Mains 2021 Hard
- If two straight lines whose direction cosines are given by the relations \(l+m-n=0,3l^{2}+m^{2}+c n l =0\) are parallel, then the positive value of \(c\) isJEE Mains 2022 Hard
- If \(7=5+\frac{1}{7}(5+\alpha)+\frac{1}{7^2}(5+2 \alpha)+\frac{1}{7^3}(5+3 \alpha)+\ldots \infty\), then the value of \(\alpha\) is :JEE Mains 2025 Medium
- Let \(P \left(\frac{2 \sqrt{3}}{\sqrt{7}}, \frac{6}{\sqrt{7}}\right), Q , R\) and \(S\) be four points on the ellipse \(9 x^2+4 y^2=36\). Let \(P Q\) and \(RS\) be mutually perpendicular and pass through the origin. If \(\frac{1}{( PQ )^2}+\frac{1}{( RS )^2}=\frac{ p }{ q }\), where \(p\) and \(q\) are coprime, then \(p+q\) is equal to \(.........\).JEE Mains 2023 Hard
- A bag contains \(6\) balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least \(5\) black balls isJEE Mains 2023 Hard
- Let \(f\) be a differentiable function satisfying \(f ( x )=\frac{2}{\sqrt{3}} \int_{0}^{\sqrt{3}} f \left(\frac{\lambda^{2} x }{3}\right) d \lambda, x >0\) and \(f (1)=\sqrt{3}\). If \(y=f(x)\) passes through the point \((\alpha, 6)\), then \(\alpha\) is equal to \(.........\)JEE Mains 2022 Hard
More PYQs from JEE Mains
- Let the solution curve \(x=x(y), 0 < y < \frac{\pi}{2}\), of the differential equation \(\left(\log _e(\cos y)\right)^2 \cos y dx -(1+3 x\) \(\left.\log _e(\cos y)\right) \sin y dy =0\) satisfy \(x\left(\frac{\pi}{3}\right)=\frac{1}{2 \log _e 2}\). If \(x\left(\frac{\pi}{6}\right)=\frac{1}{\log _e m-\log _e n}\), where \(m\) and \(n\) are co-prime, then \(mn\) is equal to \(.....\).JEE Mains 2023 Hard
- The system of equations
\(\begin{aligned}
& x+y+z=6 \\
& x+2 y+5 z=9, \\
& x+5 y+\lambda z=\mu,
\end{aligned}\) has no solution ifJEE Mains 2025 Easy - From a month of \(31\) days, \(3\) different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to \(\dfrac{a}{b}\), where \(a,b \in \mathbb{N}\) and \(\gcd(a,b)=1\), then \(a+b\) is equal to ______JEE Mains 2026 Hard
- If \(\int_{-\pi / 2}^{\pi / 2} \frac{8 \sqrt{2} \cos x d x}{\left(1+e^{\sin x}\right)\left(1+\sin ^4 x\right)}=\alpha \pi+\beta \log _e(3+2\) \(\sqrt{2}\) ), where \(\alpha, \beta\) are integers, then \(\alpha^2+\beta^2\) equals ...........JEE Mains 2024 Hard
- Let \(\vec a = 2\hat i + \hat j - 2\hat k,\vec b = \hat i + \hat j\). If \(\vec c\) is a vector such that \(\vec a.\vec c = \left| {\vec c} \right|,\left| {\vec c - \vec a} \right| = 2\sqrt 2 \) and the angle between \(\vec a \times \vec b\) and \(\vec c\) is \(30^o\), then \(\left| {\left( {\vec a \times \vec b} \right) \times \vec c} \right|\) equalsJEE Mains 2013 Hard
- If \(f\left( x \right) = {\left( {\frac{3}{5}} \right)^x} + {\left( {\frac{4}{5}} \right)^x} - 1\) , \(x \in R\) , then the equation \(f(x) = 0\) hasJEE Mains 2014 Hard