Q. The first two terms of a geometric progression add upto 12. The sum of the third and the fourth terms is 48. If terms of the geometric progression are alternately positive and negative, then the first term is
A) 4
B) $- 4$
C) $- 12$
D) 12
Explanation
(c)
Since, $a + ar = a(1 + r) = 12$ …(i)
and $ar^{2} + ar^{3} = ar^{2}(1 + r) = 48$ …(ii)
From Eqs. (i) and (ii),
$r^{2} = 4$
$\Rightarrow \ r = - 2$
(Since, the series is alternately sign, so we take negative values).
On putting the value of $r$ in Eq. (i), we get $a = - 12$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.