The sum of an infinite G. P. with positive terms is 48 and sum of its first two terms is 36. Find the second term.Choices:- 10 18 20 12

The sum of an infinite geometric progression (G.P.) is given by the formula S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio.

Given that the sum S is 48, we have:

48 = a / (1 - r) -----(1)

We're also given that the sum of the first two terms is 36. The second term of a G.P. is given by 'ar', so:

36 = a + ar -----(2)

We can solve these two equations simultaneously to find the values of 'a' and 'r', and hence find the second term 'ar'.

First, rearrange equation (1) to find 'a':

a = 48(1 - r)

Substitute this into equation (2):

36 = 48(1 - r) + 48r(1 - r)

Simplify to find 'r':

36 = 48 - 48r + 48r - 48r^2 48r^2 - 12r + 12 = 0 4r^2 - r + 1 = 0

Solving this quadratic equation gives r = 1/4 or r = 1. The common ratio of a geometric progression must be less than 1, so r = 1/4.

Substitute r = 1/4 back into equation (1) to find 'a':

48 = a / (1 - 1/4) 48 = a / 3/4 a = 48 * 3/4 = 36

Finally, the second term 'ar' is:

ar = 36 * 1/4 = 9

So, the second term of the G.P. is 9. However, this is not one of the given choices. There might be a mistake in the problem or the choices.