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JEE Main 2019 · 9 April · Shift II

JEE Main 2019 Mathematics question on Sequences and Series

If the sum and product of the first three terms in an AP are 33 and 1155, respectively, then a value of its 11th term is
  1. A.
    25
  2. B.
    -36
  3. C.
    -25
  4. D.
    -35
Show answer and solution

Correct option: C

Solution

Let the three terms be (a-d), a, (a+d).

Sum: 3a = 33 → a = 11.

Product: (11-d)(11)(11+d) = 1155 → (121 - d²) = 105 → d² = 16 → d = ±4.

For d = 4: AP is 7, 11, 15, ... → 11th term = 7 + 10(4) = 47.
For d = -4: AP is 15, 11, 7, ... → 11th term = 15 + 10(-4) = -25.

The value -25 matches option 3.

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