Question

the first term of an infinite GP exceeds the second term by 2 and its sum is 50.Find the series

Answer 1

find your attachment

Answer 2

Let the infinite GP series be a, ar, ar^2, ar^3.................................,where r be the common ratio and a be the first term of the infinite GP series. Given that the first term of the series exceeds the second term by 2, i.e.

a - ar = 2

or, a * (1 - r) = 2..........................................................(1)

And, we have the sum of the series is 50. Then,

a/ 1 - r = 50

or, a = 50 * (1 - r)

or, a = 100/ a

or, a^2 = 100

or a = 10 or -10.

taking a = 10,

From (1), 1 - r = 1/5

             or, r = 4/5

so, the series be 10, 8, 32/5.

similarly, the series can be found using a = -10.