JEE Mains · Maths · STD 11 - 8. sequence and series
The common difference of the \(A.P.\) \(b_{1}, b_{2}, \ldots,\) \(b_{ m }\) is \(2\) more than the common difference of \(A.P.\) \(a _{1}, a _{2}, \ldots, a _{ n } .\) If \(a _{40}=-159, a _{100}=-399\) and \(b _{100}= a _{70},\) then \(b _{1}\) is equal to
- A \(-127\)
- B \(-81\)
- C \(81\)
- D \(127\)
Answer & Solution
Correct Answer
(B) \(-81\)
Step-by-step Solution
Detailed explanation
\(a_{1}, a_{2}, \ldots, a_{n} \rightarrow(C D=d)\) \(b _{1}, b _{2}, \ldots, b _{ m } \rightarrow( CD = d +2)\) \(a_{40}=a+39 d=-159\) \(a_{100}=a+99 d=-399\) Subtract : \(60 d =-240 \Rightarrow d =-4\) using equation (1) \(a+39(-4)=-159\) \(a=156-159=-3\)…
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 equation of a circle is \(\operatorname{Re}\left(z^{2}\right)+2(\operatorname{Im}(z))^{2}+2 \operatorname{Re}(z)=0\), where \(z=x+\) iy. A line which passes through the center of the given circle and the vertex of the parabola, \(x^{2}-6 x-y+13=0,\) has \(y\)-intercept equal to \(.....\)JEE Mains 2021 Hard
- A stair-case of length \(l\) rests against a vertical wall and a floor of a room. Let \(P\) be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio \(1 : 2\). If the staircase begins to slide on the floor, then the locus of \(P\) isJEE Mains 2014 Hard
- If \(A = \left[ {\begin{array}{*{20}{c}}
1&{\sin \,\theta }&1\\
{ - \,\sin \,\theta }&1&{\sin \,\theta }\\
{ - 1}&{ - \,\sin \,\theta }&1
\end{array}} \right];\) then for all \(\theta \, \in \,\left( {\frac{{3\pi }}{4},\frac{{5\pi }}{4}} \right),\) det \((A)\) lies in the intervalJEE Mains 2019 Hard - Let z be a complex number such that \(|z-6|=5\) and \(|z+2-6i|=5\). Then the value of \(z^{3}+3z^{2}-15z+141\) is equal toJEE Mains 2026 Hard
- If for \(n \geq 1\) , \({P_n} = \int\limits_1^e {{{\left( {\log \,x} \right)}^n}\,dx} \) , then \(P_{10} - 90P_8\) is equal toJEE Mains 2014 Hard
- If \(A = \left[ {\begin{array}{*{20}{c}}
{\cos \,\theta }&{ - \sin \,\theta }\\
{\sin \,\theta }&{\cos \,\theta }
\end{array}} \right]\), then the matrix \({A^{ - 50}}\) when \(\theta = \frac{\pi }{{12}}\) is equal toJEE Mains 2019 Hard
More PYQs from JEE Mains
- A class contains \(b\) boys and \(g\) girls. If the number of ways of selecting \(3\) boys and \(2\) girls from the class is \(168\), then \(b +3\,g\) is equal to.JEE Mains 2022 Easy
- Let \(S=\left\{\theta \in[-\pi, \pi]-\left\{\pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\} \text {. }\) If \(T =\sum_{\theta \in S } \cos 2 \theta\), then \(T + n ( S )\) is equalJEE Mains 2022 Hard
- Let an ellipse \(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1\), \(a < b\), pass through the point \((4, 3)\) and have eccentricity \(\dfrac{\sqrt{5}}{3}\). Then the length of its latus rectum is :JEE Mains 2026 Medium
- The minimum number of elements that must be added to the relation \(R =\{( a , b ),( b , c )\}\) on the set \(\{a, b, c\}\) so that it becomes symmetric and transitive is:JEE Mains 2023 Hard
- Let \(a _{ n }\) be the \(n ^{\text {th }}\) term of the series \(5+8+14+23\) \(+35+50+\ldots\) and \(S _{ n }=\sum \limits_{ k =1}^{ n } a _{ k }\). Then \(S _{30}- a _{40}\) is equal toJEE Mains 2023 Hard
- Let \(\mathrm{x}=\frac{\mathrm{m}}{\mathrm{n}}\) ( \(\mathrm{m}, \mathrm{n}\) are co-prime natural numbers) be a solution of the equation \(\cos \left(2 \sin ^{-1} x\right)=\frac{1}{9}\) and let \(\alpha, \beta(\alpha>\beta)\) be the roots of the equation \(\mathrm{mx}^2-\mathrm{nx}-\) \(\mathrm{m}+\mathrm{n}=0\). Then the point \((\alpha, \beta)\) lies on the lineJEE Mains 2024 Medium