1. Tardigrade
  2. Question
  3. Mathematics
  4. 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

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Sequences and Series

Solution:

Since, $a+a r=a(1+r)=12 ....$(i)
and $ a r^2+a r^3=a r^2(1+r)=48 ....$(ii)
From Eqs. (i) and (ii), we get
$r^2=4 \Rightarrow r=-2$
(since the G.P. is in alternate sign, so we take negative value)
On putting the value of $r$ in Eq. (i), we get $a=-12$