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

If b is the first term of an infinite geometric progression whose sum is five, then b lies in the interval 
  1. 10, ∞
  2. -∞,-10
  3. -10, 0
  4. 0, 10

Solution

If b is the first term and r is the common ratio of an infinite G.P. and sum is 5, then

5=b1-r

⇒1-r=b5

⇒r=1-b5

⇒r=5-b5

∴-1<r<1

∴-1<5-b5<1

⇒-5<5-b<5

⇒-10<-b<0

⇒0<b<10

⇒b∈0, 10

Asked in: JEE Main 2018 (15 Apr)

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