JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(a_1, a_2, a_3 \ldots\) be in an A.P. such that \(\sum_{\mathrm{k}=1}^{12} \mathrm{a}_{2 \mathrm{k}-1}=-\frac{72}{5} \mathrm{a}_1, \mathrm{a}_1 \neq 0\). If \(\sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{a}_{\mathrm{k}}=0\), then n is:
- A 11
- B 10
- C 18
- D 17
Answer & Solution
Correct Answer
(A) 11
Step-by-step Solution
Detailed explanation
Let \(a_1=a\), common difference \(=d\) \(a_1+a_3+a_5+\ldots \ldots+a_{23}=-\frac{72}{5} a\) \(\frac{12}{2}[2 a+11 \times 2 d]=-\frac{72}{5} a\) \(12 a+132 d=-\frac{72}{5} a\) \(132 a+132 \times 5 d=0\) \(\mathrm{a}=-5 \mathrm{~d}\)…
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
- Let the vertices \(Q\) and \(R\) of the triangle \(P Q R\) lie on the line \(\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}, Q R=5\) and the coordinates of the point \(P\) be \((0,2,3)\). If the area of the triangle \(P Q R\) is \(\frac{m}{n}\) then :JEE Mains 2025 Medium
- The distance of the point \((1,1,9)\) from the point of intersection of the line \(\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}\) and the plane \(x+y+z=17\) isJEE Mains 2021 Medium
- If the area of the region \(\left\{( x , y ):\left| x ^2-2\right| \leq y \leq x \right\}\) is \(A\), then \(6 A +16 \sqrt{2}\) is equal to \(...........\).JEE Mains 2023 Hard
- If a hyperbola has length of its conjugate axis equal to \(5\) and the distance between its foci is \(13\), then the eccentricity of the hyperbola isJEE Mains 2019 Hard
- Let \(f: R \rightarrow R\) be a function defined as \(f(x)=\left\{\begin{array}{cl}\frac{\sin (a+1) x+\sin 2 x}{2 x} & , \text { if } x<0 \\ b & , \text { if } x=0 \\ \frac{\sqrt{x+b x^{3}}-\sqrt{x}}{b x^{5 / 2}} & , \text { if } x>0\end{array}\right.\) . If \(f\) is continuous at \(x=0,\) then the value of \(a + b\) is equal to ....... .JEE Mains 2021 Hard
- For a differentiable function \(\mathrm{f}: I R \rightarrow I R\), suppose \(f^{\prime}(\mathrm{x})=3 f(\mathrm{x})+\alpha\), where \(\alpha \in \operatorname{IR}, f(0)=1\) and \(\lim _{x \rightarrow-\infty} f(x)=7\). Then \(9 \mathrm{f}\left(-\log _{\mathrm{e}} 3\right)\) is equal to ............JEE Mains 2024 Hard
More PYQs from JEE Mains
- Let the length of the latus rectum of an ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) \( (a>b) \), be 30. If its eccentricity is the maximum value of the function \( f(t)=-\frac{3}{4}+2t-t^{2}, \) then \( (a^{2}+b^{2}) \) is equal to -JEE Mains 2026 Medium
- The differential equation of the family of circles passing the origin and having center at the line \(y=x\) is :JEE Mains 2024 Hard
- The number of seven digit positive integers formed using the digits \(1,2,3\) and \(4\) only and sum of the digits equal to \(12\) is \(...........\).JEE Mains 2023 Hard
- The plane passing through the poin \((4, -1, 2)\) and parallel to the lines \(\frac{{x + 2}}{3} = \frac{{y - 2}}{{ - 1}} = \frac{{z + 1}}{2}\) and \(\frac{{x - 2}}{1} = \frac{{y - 3}}{2} = \frac{{z - 4}}{3}\) also passes through the pointJEE Mains 2019 Hard
- A triangle \(ABC\) lying in the first quadrant has two vertices as \(A (1,2)\) and \(B (3,1)\). If \(\angle BAC =90^{\circ},\) and \(\operatorname{ar}(\Delta ABC )=5 \sqrt{5}\) sq. units then the abscissa of the vertex \(C\) isJEE Mains 2020 Hard
- The number of the real solutions of the equation : \( x|x+3|+|x-1|-2=0 \) isJEE Mains 2026 Easy