Q. Three numbers form a GP. If the 3rd term is decreased by 64, then the three numbers thus obtained will constitute an AP. If the second term of this AP is decreased by 8, a GP will be formed again, then the numbers will be
A) 4, 20, 36
B) 4, 12, 36
C) 4, 20, 100
D) None of these
Explanation
(c)
Let $a,\ ar,\ ar^{2}$ are in GP $a,\ ar,\ ar^{2} - 64$ are in AP, we get
$a\left( r^{2} - 2r + 1 \right) = 64$ …(i)
Again, $a,\ ar - 8,\ ar^{2} - 64$ are in GP.
$\therefore(ar - 8)^{2} = a(ar^{2} - 64)$
$\Rightarrow a(16r - 64) = 64$ …(ii)
On solving Eqs. (i) and (ii), we get $r = 5,\ a = 4$
Thus, required numbers are 4, 20, 100
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.