# ISI2017-DCG-8

0 votes
50 views

If $x,y,z$ are in $A.P.$ and $a>1$, then $a^x, a^y, a^z$ are in

1. $A.P.$
2. $G.P$
3. $H.P$
4. none of these

recategorized

## 1 Answer

1 vote

Answer: $\mathbf B$

Solution:

Let $a = 2$

and, $\mathrm{x = 4, y = 6, z = 8}$ be the terms in $\mathbf {AP}$ with common difference $=2$

Now,

$\mathrm{a^x = 4^2, a^y = 4^4, a^z = 4^6}$

$\mathrm {\frac{a^y}{a^x} = \frac{4^4}{4^2} = 16,\;\text{and} \;\frac{a^z}{a^y} = \frac{4^6}{4^4} = 16}$

So, the resultant terms are in $\mathbf GP$

$\therefore \mathbf B$ is the correct option.

edited by

## Related questions

0 votes
1 answer
1
37 views
If $a,b,c$ are in $A.P.$ , then the straight line $ax+by+c=0$ will always pass through the point whose coordinates are $(1,-2)$ $(1,2)$ $(-1,2)$ $(-1,-2)$
1 vote
2 answers
2
112 views
The value of $\dfrac{1}{\log_2 n}+ \dfrac{1}{\log_3 n}+\dfrac{1}{\log_4 n}+ \dots + \dfrac{1}{\log_{2017} n}\:\:($ where $n=2017!)$ is $1$ $2$ $2017$ none of these
0 votes
2 answers
3
78 views
The area of the shaded region in the following figure (all the arcs are circular) is $\pi$ $2 \pi$ $3 \pi$ $\frac{9}{8} \pi$
0 votes
1 answer
4
53 views
The sum of the squares of the roots of $x^2-(a-2)x-a-1=0$ becomes minimum when $a$ is $0$ $1$ $2$ $5$