Q44 / 90 · JEE Main 2018 (15 Apr) · Mathematics

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

  • A
    10, ∞
  • B
    -∞,-10
  • C
    -10, 0
  • Correct answer
    D
    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

Hence, the correct answer is option: 'D'.

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