JEE Mains · Maths · STD 11 - 8. sequence and series
The sum of the first \(20\) terms of the series \(5+11+\) \(19+29+41+\ldots\) is \(..........\).
- A \(3450\)
- B \(3250\)
- C \(3420\)
- D \(3520\)
Answer & Solution
Correct Answer
(D) \(3520\)
Step-by-step Solution
Detailed explanation
\(S _{20}=5+11+19+29+\ldots \ldots\) Let \(T _{ r }=a r^2+ br + c\) \(T _1= a + b + c =5\) \(T _2=4 a +2 b + c =11\) \(T _3=9 a +3 b + c =19\) \(a =1, b =3, c =1\) Hence \(S _{20}=\sum_{ r =1}^{20} r ^2+3 \sum_{ r =1}^{20} r +\sum_{ r =1}^{20} 1=3520\)
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
- If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, isJEE Mains 2015 Hard
- Let \(a_{1}, a_{2}, \ldots \ldots, a_{21}\) be an \(A.P.\) such that \(\sum_{n=1}^{20} \frac{1}{a_{n} a_{n+1}}=\frac{4}{9}\). If the sum of this AP is \(189,\) then \(a_{6} \mathrm{a}_{16}\) is equal to :JEE Mains 2021 Hard
- Let \(A\) and \(B\) be two invertible matrices of order \(3 \times 3\). If det \((ABA^T) = 8\) and \(det\,(AB^{-1}) = 8\), then \(det\, (BA^{-1} B^T)\) is equal toJEE Mains 2019 Hard
- A wire of length \(20\, \mathrm{~m}\) is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the side (in \(meters\)) of the hexagon, so that the combined area of the square and the hexagon is minimum, is:JEE Mains 2021 Hard
- If \('R'\) is the least value of \('a'\) such that the function \(\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}+\mathrm{ax}+1\) is increasing on \([1,2]\) and \('\mathrm{S}^{\prime}\) is the greatest value of \('a'\) such that the function \(f(x)=x^{2}+a x+1\) is decreasing on \([1,2]\), then the value of \(|\mathrm{R}-\mathrm{S}|\) is ..... .JEE Mains 2021 Hard
- In the figure, \(\theta_1+\theta_2=\frac{\pi}{2}\) and \(\sqrt{3}(B E)=4(A B)\). If the area of \(\triangle CAB\) is \(2 \sqrt{3}-3\) unit \(^2\), when \(\frac{\theta_2}{\theta_1}\) is the largest, then the perimeter (in unit) of \(\triangle CED\) is equal to \(...........\).
JEE Mains 2023 Hard
More PYQs from JEE Mains
- Let \( y=y(x) \) be the solution of the differential equation \( secx\frac{dy}{dx}-2y=2+3~sin~x, x\in(-\frac{\pi}{2},\frac{\pi}{2}), \) \( y(0)=-\frac{7}{4}. \) Then \( y(\frac{\pi}{6}) \) is equal to :JEE Mains 2026 Hard
- Let \(y = y ( x )\) be the solution of the differential equation \(x d y-y d x=\sqrt{\left(x^{2}-y^{2}\right)} d x, x \geq 1\), with \(y (1)=0 .\) If the area bounded by the line \(x =1, x = e ^{\pi}, y =0\) and \(y = y ( x )\) is \(\alpha e ^{2 \pi}+\beta\) then the value of \(10(\alpha+\beta)\) is equal to ....... .JEE Mains 2021 Medium
- Two poles, \(\mathrm{AB}\) of length \(a\) metres and \(\mathrm{CD}\) of length \(\mathrm{a}+\mathrm{b}(\mathrm{b} \neq \mathrm{a})\) metres are erected at the same horizontal level with bases at \(\mathrm{B}\) and \(\mathrm{D} .\) If \(\mathrm{BD}=\mathrm{x}\) and \(\tan \angle\,ACB=\frac{1}{2}\), then:JEE Mains 2021 Hard
- Let \(x\) and \(y\) be distinct integers where \(1 \leq x \leq 25\) and \(1 \leq y \leq 25\). Then, the number of ways of choosing \(x\) and \(y\), such that \(x + y\) is divisible by \(5\) , is \(.........\).JEE Mains 2023 Hard
- The integral \(\int {\frac{{{{\sin }^2}\,x\,{{\cos }^2}\,x}}{{({{\sin }^3}\,x\, + {{\cos }^3}\,x)^2}}} dx\) is equal toJEE Mains 2014 Hard
- For which of the following ordered pairs \((\mu, \delta)\) the system of linear equations \(x+2 y+3 z=1\) ; \(3 x+4 y+5 z=\mu\) ; \(4 x+4 y+4 z=\delta\) is inconsistent?JEE Mains 2020 Hard