1. Tardigrade
  2. Question
  3. Mathematics
  4. The sum of first two terms of a geometric progression is 12. The sum of the third and the fourth terms is 48. If the 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 sum of first two terms of a geometric progression is 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative then the first term is

Sequences and Series

Solution:

Let $a, a r, a r^2, a r^3$ ......
$a+a r=12 $ ......(I)
$a r^2+a r^3=48$ .......(II)
(I) $\div$ (II) $\frac{ a (1+ r )}{ ar ^2(1+ r )}=\frac{12}{48} \Rightarrow \frac{1}{ r ^2}=\frac{1}{4}$
$r = \pm 2$
Terms altemately positive and negative
$\therefore r =-2$
From equation (I) $- a =12 \Rightarrow a =-12$.