Verified Solution • 2025–26 Session moderate

QJEEM20Ma34f6: JEE Main 2020 Mathematics - Class 11 JEEM20Ma34f6 Solution: If the first term of an A.P. is 3 and the sum of its first 25…

If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is :

Multiple Choice Options

  • A 14{1 \over 4}
  • B 15{1 \over 5}
  • C 17{1 \over 7}
  • D 16{1 \over 6}

Step-by-Step Verified Solution

First 25 terms = a, a + d, .......,a + 24d

Next 15 terms = a + 25d, a + 26d, ......, a + 39d

∴\therefore 252[2a+24d]=152[2(a+25d)+14d]{{25} \over 2}\left[ {2a + 24d} \right] = {{15} \over 2}\left[ {2\left( {a + 25d} \right) + 14d} \right]

⇒\Rightarrow 50a + 600d = 15 [2a + 50d + 14d]

⇒\Rightarrow 20a + 600d = 960d

⇒\Rightarrow 60 = 360d

⇒\Rightarrow d = 16{1 \over 6}

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