like progressions???

Algebra Level 4

a, b, c are positive integers that are in a geometric progression where the common ratio is an integer. If A.M of a,b,c = b+2;

Find the smallest possible value of $a$ .

1 solution

Department 8
Sep 13, 2015

If $a,b,c$ is in geometric progression then let their common ratio be $r$ . Then

$b=ar\\ c=ar^{2}$

Now about given mean,

$a+ar+ar^{2} = 3(ar+2) \\ ar^{2}+ar+a=3ar+6\\ ar^{2}-2ar+a=6\\ (r-1)^{2}=\frac{6}{a} \\ r=\sqrt{\frac{6}{a}} +1$

Now you can apply some number theory over here to get $\boxed{a=6}$

purusharth ,where did you get this question? Do you consider it a level 4 problem??

rahul saxena - 5 years, 9 months ago

r=2 did it

Kaustubh Miglani - 5 years, 8 months ago