AP EAMCET · Maths · Sequences and Series
If \(2.5+5.9+8.13+11.17+\ldots\) to n terms \(=\mathrm{an}^3+\mathrm{bn}^2+\mathrm{cn}+\mathrm{d}\), then \(a-b+c-d=\)
- A 7
- B 5
- C -3
- D -1
Answer & Solution
Correct Answer
(D) -1
Step-by-step Solution
Detailed explanation
\(T_n = (3n-1)(4n+1) = 12n^2-n-1\) \(S_n = \sum_{k=1}^{n} (12k^2-k-1) = 12\frac{n(n+1)(2n+1)}{6} - \frac{n(n+1)}{2} - n\) \(S_n = 4n^3+6n^2+2n - \frac{1}{2}n^2-\frac{1}{2}n - n = 4n^3+\frac{11}{2}n^2+\frac{1}{2}n\) \(a=4, b=\frac{11}{2}, c=\frac{1}{2}, d=0\)…
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 probabilities that A and B speak truth are and respectively. The probability that they contradict each other when asked to speak on a fact isAP EAMCET 2021 Easy
- If \(A\) and \(B\) are two independent events such that \(P(B)=\frac{2}{7}, P\left(A \cup B^c\right)=0.8\), then \(P(A)\) is equal to :AP EAMCET 2006 Medium
- \(A(3,2,-1), B(4,1,1), C(6,2,5)\) and \(D(3,3,3)\) are four points. \(G_1, G_2, G_3\) and \(G_4\) respectively are the centroids of the triangles \(\triangle B C D, \triangle C D A\), \(\triangle D A B\) and \(\triangle A B C\). The point of concurrence of the lines \(A G_1, B G_2, C G_3\) and \(D G_4\) isAP EAMCET 2018 Easy
- AP EAMCET 2019 Medium
- \([\mathrm{t}]\) denotes the greatest integer function and \([\mathrm{t}-\mathrm{m}]=[\mathrm{t}]-\mathrm{m}\) when \(\mathrm{m} \in \mathrm{Z}\). If \(\mathrm{k}=2[2 \mathrm{x}-1]-1\) and \(3[2 \mathrm{x}-2]+1=2[2 \mathrm{x}-1]-1\) then the range of \(\mathrm{f}(\mathrm{x})=\) \([\mathrm{k}+5 \mathrm{x}]\) isAP EAMCET 2025 Medium
- If \(f: R \rightarrow R\) is defined by
\(f(x)=\left\{\begin{array}{cc}
\frac{2 \sin x-\sin 2 x}{2 x \cos x}, & \text { if } x \neq 0 \\
a, & \text { if } x=0
\end{array}\right. \text {, }\)
then the value of \(a\) so that \(f\) is continuous at 0 isAP EAMCET 2009 Medium
More PYQs from AP EAMCET
- The element with highest electronegativity value after fluorine isAP EAMCET 2022 Easy
- The wavelength of maximum emitted energy \(\left(\lambda_m\right)\) of a body at \(700 \mathrm{~K}\) is \(4.08 \mu \mathrm{m}\). If the temperature of the body is raised to \(1400 \mathrm{~K}\), then the value of \(\lambda_m\) will beAP EAMCET 2020 Medium
- The experimentally determined molar mass of a non-volatile solute, \(\mathrm{BaCl}_2\) in water by Cottrell's method, isAP EAMCET 2012 Medium
- If a system of three linear equations in three unknowns, which is in the matrix equation form of \(A X=D\), is inconsistent, then \(\frac{\text { rank of } A}{\text { rank of } A D}\) isAP EAMCET 2017 Easy
- In \(\triangle A B C, \angle A=90^{\circ}\) and co-ordinates of points \(B\) and \(C\) are \((2,-4)\) and \((1,5)\). Then the equation of the circumcircle of \(\triangle A B C\) isAP EAMCET 2020 Medium
- The coefficient of \(x^n\) in \(\frac{1-2 x}{e^x}\) is :AP EAMCET 2006 Medium