Question

The sum of an infinite G.P. with positive terms is 48, and the sum of its first two terms is 36. Find the second term.

a. 6
b. 8
c. 12
d. 18

Answer 1

The second term of the infinite G.P. with a sum of 48 and the sum of the first two terms being 36 is 12.

correct option is c. 12

Step-by-step explanation:

Let the first term of the infinite G.P. be 'a' and the common ratio be 'r'. Since the sum of infinite G.P. with positive terms is given by S = a / (1-r), and the given sum S is 48, we have a / (1-r) = 48. Also, the sum of the first two terms is a + ar, which is given to be 36. That means a(1 + r) = 36.

Now we have two equations:

1. a / (1-r) = 48,
2. a(1 + r) = 36.

From the first equation, we can express 'a' as a = 48(1-r). Substituting this into the second equation, we get 48(1-r)(1 + r) = 36. Simplifying, we find that r = 1/2. Now we can go back and find 'a' from the first equation: a = 48(1 -1/2) = 48/2 = 24. Then the second term, which is ar, is 24 x 1/2 = 12.

Therefore, the second term of the G.P. is 12, which corresponds to option c.