WBJEE · Maths · Sequences and Series
Given an A.P. and a G.P. with positive terms, with the first and second terms of the progressions being equal. If \(a_n\) and \(b_n\) be the \(n^{\text {th }}\) term of A.P. and G.P. respectively then
- A \(a_n \gt b_n\) for all \(n \gt 2\)
- B \(a_n \lt b_n\) for all \(n \gt 2\)
- C \(a_n=b_n\) for some \(n \gt 2\)
- D \(a_n=b_n\) for some odd \(n\)
Answer & Solution
Correct Answer
(B) \(a_n \lt b_n\) for all \(n \gt 2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Hint: } a_1, a_2, a_3, \ldots \ldots, a_n \rightarrow \text { AP } \\ & a_1, a_2, b_3, \ldots \ldots, b_n \rightarrow G P \\ & a_n=a_1+(n-1)\left(a_2-a_1\right) \\ & b_n=a_1\left(\frac{a_2}{a_1}\right)^{n-1}=a_2^{n-1} \cdot a_1^{1-n+1}=a_2^{n-1} \cdot…
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 \(p, q\) and \(r\) be the altitudes of a triangle with area \(S\) and perimeter \(2 t .\) Then, the value of \(\frac{1}{p}+\frac{1}{q}+\frac{1}{r}\) isWBJEE 2012 Easy
- If \(f(x)=\sin x+2 \cos ^{2} x, \frac{\pi}{4} \leq x \leq \frac{3 \pi}{4} .\) Then, \(f\) attains itsWBJEE 2013 Medium
- A particle starts at the origin and moves l unit horizontally to the right and reaches \(P_{1}\), then it moves \(\frac{1}{2}\) unit vertically up and 2 reaches \(P_{2}\), then it moves \(\frac{1}{4}\) unit horizontally to right and reaches \(P_{3}\), then it moves \(\frac{1}{8}\) unit vertically down and reaches \(P_{4}\), then it moves \(\frac{1}{16}\) unit horizontally to right and reaches \(P_{\mathrm{S}}\) and so on. Let \(P_{n}=\left(x_{n}, y_{n}\right)\) and \(\lim _{n \rightarrow \infty} x_{n}=\alpha\) and \(\lim _{n \rightarrow \infty} y_{n}=\beta .\) Then, \((\alpha, \beta)\) isWBJEE 2019 Medium
- If \(\log _{e}\left(x^{2}-16\right) \leq \log _{e}(4 x-11)\), thenWBJEE 2012 Easy
- Rolle's theorem is applicable in the interval [-2,2] for the functionWBJEE 2012 Easy
- If \(e^{\sin x}-e^{-\sin x}-4=0,\) then the number ofreal values of \(x\) isWBJEE 2019 Medium
More PYQs from WBJEE
- If \(\frac{\mathrm{d}}{\mathrm{dx}}\{\mathrm{f}(\mathrm{x})\}=\mathrm{g}(\mathrm{x})\), then \(\int_a^b \mathrm{f}(\mathrm{x}) \mathrm{g}(\mathrm{x}) \mathrm{dx}\) is equal toWBJEE 2010 Medium
- Sand \(T\) are the foci of an ellipse and \(B\) is the end point of the minor axis. If \(S T B\) is equilateral triangle, the eccentricity of the ellipse isWBJEE 2019 Easy
- ADP and ATP differ in the number ofWBJEE 2017 Easy
- Let \(P(x)\) be a polynomial, which when \(\begin{array}{llll}\text { divided by } & (x-3) & \text { and } & (x-5) & \text { leaves }\end{array}\) remainders 10 and 6, respectively. If the polynomial is divided by \((x-3)(x-5),\) thes the remainder isWBJEE 2015 Easy
- The vectors \(\mathrm{A}\) and \(\mathrm{B}\) are such that \(|\mathbf{A}+\mathbf{B}|=|\mathbf{A}-\mathbf{B}| .\) The angle between the two vectors will beWBJEE 2016 Medium
- The effective resistance between \(A\) and \(B\) in the figure is \(\frac{7}{12} \Omega\) if each side of the cube has \(1 \Omega\) resistance. The effective resistance between the same two points, when the link \(A B\) is removed, is
WBJEE 2016 Medium