Question

The sum of an infinite G.P. whose common ratio is positive and is numerically less than 1 is 36 and the sum of the first two terms is 32. What will be the third term?

(a) 1/3
(b) 4/3
(c) 8 /3
(d) 2

Answer 1

To find the third term of the infinite geometric progression, we need to find the common ratio and the first term.

By solving the given equations, we determine that the common ratio is 1/3 and the first term is 36. Using the formula for the third term, we calculate that it is 4/3.

Step-by-step explanation:

To find the third term of the infinite geometric progression (G.P.), we first need to find the common ratio (r) and the first term (a).

Given that the sum of the G.P. is 36 and the sum of the first two terms is 32, we can set up the following equation:

a(1 - r^2) / (1 - r) = 32

Using the formula for the sum of an infinite G.P., we have:

a / (1 - r) = 36

Simplifying the equations, we get:

32(1 - r) = a(1 - r^2)

36(1 - r) = a

By solving these equations, we find that r = 1/3 and a = 36.

The third term of the G.P. can be calculated using the formula:

a * r^2 = 36 * (1/3)^2 = 4/3.

Therefore, the third term is 4/3.