If b is the first term of an infinite geometric progression whose sum is five, then b lies in the interval

Step-by-step solution

If b is the first term and r is the common ratio of an infinite G.P. and sum is 5 , then 5 = b 1 - r ⇒ 1 - r = b 5 ⇒ r = 1 - b 5 ⇒ r = 5 - b 5 ∴ - 1 < r < 1 ∴ - 1 < 5 - b 5 < 1 ⇒ - 5 < 5 - b < 5 ⇒ - 10 < - b < 0 ⇒ 0 < b < 10 ⇒ b ∈ 0 ,   10