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 1

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:

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

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

From equation (2), we can express 'a' in terms of 'r':

a = 36 - ar

Substitute this into equation (1):

48 = (36 - ar) / (1 - r)

Solving this equation gives r = 0.5.

Substitute r = 0.5 into equation (2) to find 'a':

a + 0.5a = 36 1.5a = 36 a = 36 / 1.5 = 24

The second term 'ar' is therefore:

ar = 24 * 0.5 = 12

So, the second term of the G.P. is 12, which is not in the given choices. There might be a mistake in the problem or the choices.