Question

The first two terms of a G.P. add up to 12. The sum of
the third and the fourth terms is 48. If the terms of the
G.P. are alternately positive and negative, then the first
term is:
(A) 4
(B) -12
(C) 12
(D) 4​

Answer 1

Answer:

the correct answer is -12 i.e., b option

Answer 2

Let the first term of the GP, be 'a' and the common ratio be 'r'

So According to the Question

we have

$a + ar = 12..(1)$

$a {r}^{2} + a {r}^{3} = 48..(2)$

After Solving (1) and (2)

$\frac{1}{2} = \frac{1}{ {r}^{2} } = \frac{1}{4}$

$r²=4$

we get

$r = ±2$

But, as the terms are alternative positive and negative

∴r is negative

That Means

$r = - 2$

Now, Putting r=-2 in equation (1)

$a + - 2a = 12$

$= > - a = 12$

$= > a = - 12$

Option b)-12 is the Correct answer