GATE Overflow Test Series | Quantitative Aptitude | Test 1 | Question: 17

Question

The $4^{\text{th}}$ term of a G.P. is $25$ and its $6^{\text{th}}$ term is $64,$ then the common ratio of the G.P. is ________

• A. $\pm \dfrac{8}{5}$
• B. $\dfrac{1}{8}$
• C. $\pm \dfrac{5}{8}$
• D. $\pm \dfrac{64}{25}$

Answer 1

We know that $n^{\text{th}}$ term of the GP $:a_{n}  = a\times r^{n-1},$ where $a = $ first term, $r = $ common ratio

Now, $T_{4} = ar^{3} = 25\qquad \rightarrow(1)$

and $T_{6} = ar^{5} = 64\qquad \rightarrow(2)$

Dividing equation $(2)$ by equation $(1),$ we get

$\dfrac{ar^{5}}{ar^{3}} = \dfrac{64}{25}$

$\implies r^{2} = \left(\dfrac{8}{5} \right)^{2}$

$\implies r = \pm \dfrac{8}{5}.$

So, the correct answer is $(A).$

Comments

Small typo after division.

It will be    a(r^5) / a(r^3)