WBJEE · Maths · Sequences and Series
Five numbers are in AP with common difference \(\neq 0 .\) If the 1 st, 3 rd and 4 th terms are in GP, then
- A the 5th term is always \(0 .\)
- B the 1 st term is always \(0 .\)
- C the middle term is always \(0 .\)
- D the middle term is always -2.
Answer & Solution
Correct Answer
(A) the 5th term is always \(0 .\)
Step-by-step Solution
Detailed explanation
Let the tine number is in AP are \[ (a-2 d),(a-d), a,(a+d),(a+2 d) \] where, \(d \neq 0\) Given, 1 st, \(3 r d\) and 4 th terms are in GP.…
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 \(\alpha\) and \(\beta\) be the roots of \(x^{2}+x+1=0 .\) If \(n\) be a positive integer, then \(\alpha^{n}+\beta^{n}\) isWBJEE 2017 Medium
- The locus of points \((x, y)\) in the plane satisfying \(\sin ^2 x+\sin ^2 y=1\) consists ofWBJEE 2023 Hard
- Let \(\mathrm{A}=\left(\begin{array}{ccc}1 & -1 & 0 \\ 0 & 1 & -1 \\ 1 & 1 & 1\end{array}\right), \mathrm{B}=\left(\begin{array}{l}2 \\ 1 \\ 7\end{array}\right)\)
Then for the validity of the result \(\mathrm{AX}=\mathrm{B}, \mathrm{X}\) isWBJEE 2024 Easy - Consider the function \(f(x)=\cos x^{2}\). Then,WBJEE 2019 Easy
- If the matrices \(A=\left[\begin{array}{lll}2 & 1 & 3 \\ 4 & 1 & 0\end{array}\right]\) and \(B=\left[\begin{array}{rr}1 & -1 \\ 0 & 2 \\ 5 & 0\end{array}\right]\), then \(\mathrm{AB}\) will beWBJEE 2010 Easy
- Let \(f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x^3 & 2 x \\ \tan x & x & 1\end{array}\right|\), then \(\lim _{x \rightarrow 0} \frac{f(x)}{x^2}=\)WBJEE 2024 Medium
More PYQs from WBJEE
- If \(I=\int_{0}^{2} e^{x^{4}}(x-a) d x=0\), then \(\alpha\) lies in the intervalWBJEE 2014 Medium
- If angles \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are in A.P., then \(\frac{\mathrm{a}+\mathrm{c}}{\mathrm{b}}\) is equal toWBJEE 2010 Hard
- What is the four-electron reduced form of \(\mathrm{O}_2\) ?WBJEE 2025 Easy
- Let the equation of an ellipse be \(\frac{x^{2}}{144}+\frac{y^{2}}{25}=1\) Then, the radius of the circle with centre \((0, \sqrt{2})\) and passing through the foci of the ellipse isWBJEE 2014 Medium
- \(1 \times 10^{-3}\) mole of \(\mathrm{HCl}\) is added to a buffer solution made up of \(0.01 \mathrm{M}\) acetic acid and 0.01 M sodium acetate. The final pH of the buffer will be (given, \(\mathrm{p} K_{a}\) of acetic acid is 4.75 at \(\left.25^{\circ} \mathrm{C}\right)\)WBJEE 2013 Hard
- Angle between \(\mathrm{y}^2=\mathrm{x}\) and \(\mathrm{x}^2=\mathrm{y}\) at the origin isWBJEE 2009 Medium