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JEE Main202310 Apr 2023Morning ShiftMathematicsSequences and SeriesActual

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033 , then the sum of these three terms is equal to

Options

  1. A241
  2. B231
  3. C210
  4. D220

Correct answer

B. 231

Step-by-step solution

Given that, a 2 + a r 2 + a r 2 2 = 33033 ,   a , r ∈ N ⇒ a 2 1 + r 2 + r 4 = 11 2 × 273 On comparing both sides of the equation we get, a = 11 and 1 + r 2 + r 4 = 273 ⇒ r 2 + r 4 = 272 ⇒ r 2 1 + r 2 = 16 × 17 ⇒ r = 4 Now a + a r + a r 2 = 11 + 11 × 4 + 11 × 16 = 11 + 44 + 176 = 231 . Therefore, the required value is 231

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