Verified Solution • 2025–26 Session moderate

QJEEM18Mae62f: JEE Main 2018 Mathematics - Class 11 JEEM18Mae62f Solution: If b is the first term of an infinite G.P. whose sum is five,…

If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

Multiple Choice Options

  • A ( −- ∞\infty , −- 10]
  • B ( −- 10, 0)
  • C (0, 10)
  • D [10, ∞\infty )

Step-by-Step Verified Solution

Sum of infinite G.P,

S = b1−rb \over {1-r} where \left| r \right| < 1

⇒\Rightarrow 5 = b1−rb \over {1-r}

⇒\Rightarrow 1 - r = b5b \over 5

⇒\Rightarrow b = 5(1 - r)

as \left| r \right| < 1

∴\therefore  -1 < r < 1

⇒\Rightarrow 1 > -r > -1

⇒\Rightarrow 2 > 1-r > 0

⇒\Rightarrow 10 > 5(1-r) > 0

⇒\Rightarrow 10 > b > 0

∴\therefore interval of b = (0, 10)

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