If the $${2^{nd}},{5^{th}}$$ and $${9^{th}}$$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:
A.
$$1$$
B.
$$\frac{7}{4}$$
C.
$$\frac{8}{5}$$
D.
$$\frac{4}{3}$$
Answer :
$$\frac{4}{3}$$
Solution :
$$\eqalign{
& {\text{Let the G}}{\text{.P}}{\text{. be }}a,ar{\text{ and }}a{r^2}{\text{ then }}a = A + d;ar = A + 4d; \cr
& a{r^2} = A + 8d \cr
& \Rightarrow \,\,\frac{{a{r^2} - ar}}{{ar - a}} = \frac{{\left( {A + 8d} \right) - \left( {A + 4d} \right)}}{{\left( {A + 4d} \right) - \left( {A + d} \right)}} \cr
& r = \frac{4}{3} \cr} $$
Releted MCQ Question on Algebra >> Sequences and Series
Releted Question 1
If $$x, y$$ and $$z$$ are $${p^{{\text{th}}}},{q^{{\text{th}}}}\,{\text{and }}{r^{{\text{th}}}}$$ terms respectively of an A.P. and also of a G.P., then $${x^{y - z}}{y^{z - x}}{z^{x - y}}$$ is equal to:
If $$a, b, c$$ are in G.P., then the equations $$a{x^2} + 2bx + c = 0$$ and $$d{x^2} + 2ex + f = 0$$ have a common root if $$\frac{d}{a},\frac{e}{b},\frac{f}{c}$$ are in-