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

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

Tardigrade Admin · Accepted Answer

Since, a+a r=a(1+r)=12 ....(i) and a r2+a r3=a r2(1+r)=48 ....(ii) From Eqs. (i) and (ii), we get r2=4 ⇒ 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

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

4

$- 4$

$- 12$

12

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 $a = - 12$

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

4

−4

−12

12

Since, a+ar=a(1+r)=12....(i) and ar2+ar3=ar2(1+r)=48....(ii) From Eqs. (i) and (ii), we get r2=4⇒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

$- 4$

$- 12$

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 $a = - 12$