WBJEE · Maths · Sequences and Series
In a GP series consisting of positive terms, each term is equal to the sum of next two terms. Then, the common ratio of this GP series is
- A \(\sqrt{5}\)
- B \(\frac{\sqrt{5}-1}{2}\)
- C \(\frac{\sqrt{5}}{2}\)
- D \(\frac{\sqrt{5}+1}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{\sqrt{5}-1}{2}\)
Step-by-step Solution
Detailed explanation
Let \(a_{n}\) be the general term of a GP whose first term is \(a\) and common ratio is \(r\). Now according to the question, \[ \begin{aligned} a_{n} &=a_{n+1}+a_{n+2} \\ a r^{n-1} &=a r^{n}+a r^{n+1} \end{aligned} \] \(\Rightarrow \quad r^{n-1}=r^{n}+r^{n+1}\)…
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 \(f:[a, b] \rightarrow \mathbb{R}\) be continuous in \([a, b]\), differentiable in \((a, b)\) and \(f(a)=0=f(b)\). ThenWBJEE 2022 Medium
- The minimum value of \(f(x)=e^{\left(x^4-x^3+x^2\right)}\) isWBJEE 2010 Medium
- Let \(f(x)=a_0+a_1|x|+a_2|x|^2+a_3|x|^3\), where \(a_0, a_1, a_2, a_3\) are real constants. Then \(f(x)\) is differentiable at \(x=0\)WBJEE 2022 Medium
- If \(\alpha\) and \(\beta\) are roots of \(a x^{2}+b x+c=0,\) then
the equation whose roots are \(\alpha^{2}\) and \(\beta^{2},\) isWBJEE 2016 Easy - \(\int \frac{x^3 d x}{1+x^8}=\)WBJEE 2011 Hard
- Let \(A=\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \text { cost } & \text { sint } \\ 0 & -\sin t & \cos t\end{array}\right)\)
Let \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) be the roots of \(\operatorname{det}\left(A-\lambda I_{3}\right)=0\), where \(I_{3}\) denotes the identity matrix. If \(\lambda_{1}+\lambda_{2}+\lambda_{3}=\sqrt{2}+1\), then the set of possible values of \(t,-\pi \leq t < \pi\) isWBJEE 2021 Hard
More PYQs from WBJEE
- To write the decimal number 37 in binary, how many binary digits are required?WBJEE 2009 Hard
- \[
\text { In the figure below, the capacitance of each capacitor is } 3 \mu \mathrm{F} \text {. The effective capacitance between } \mathrm{A} \text { and } \mathrm{B} \text { is : }
\]
WBJEE 2010 Medium - Six vectors \(\vec{a}, \vec{b}, \vec{c}, \vec{d}, \vec{e}\) and \(\vec{f}\) have the magnitudes and directions indicated in the figure. Which of the following statements is true?
WBJEE 2025 Easy - The total number of isomeric linear dipeptides which can be synthesised from racemic alanine isWBJEE 2019 Hard
- p-nitro-N, N - dimethylaniline cannot be represented by the resonating structures
WBJEE 2021 Medium - If one of the diameters of the curve \(x^{2}+y^{2}-4 x-6 y+9=0\) is a chord of a circle with centre \((1,1),\) the radius of this circle isWBJEE 2017 Easy