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Sequences and Series

JEE Main 2024 (Online) 27th January Morning ShiftMCQEasy📈 Topic in 57% papers+4−1
Ques. 1JEE Main 2024, 27 January (Morning Shift)

The number of common terms in the progressions 4, 9, 14, 19, , up to 25th term and 3, 6, 9, 12, , up to 37th term is :

  1. 9
  2. 8
  3. 5
  4. 7

Answer

(4) 7

Solution

Last terms: T25=4+24 5=124, T37=3+36 3=111

∵ common terms form an A.P. with d=LCM(5, 3)=15, first common term =9

⇒ common terms: 9, 24, 39, up to 111 (the smaller last term)

9+15(m-1) 111 ⇒ m-1 6.8 ⇒ m=7

(terms 9, 24, 39, 54, 69, 84, 99)

Answer: (4)

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Ques. 2JEE Main 2024, 27 January (Morning Shift)

If 8=3+ 14(3+p)+ 142(3+2p)+ 143(3+3p)+ , then the value of p is .

Ques. 3JEE Main 2024, 27 January (Evening Shift)

The 20th term from the end of the progression 20, 19 14, 18 12, 17 34, , -129 14 is :

  1. -115
  2. -100
  3. -110
  4. -118

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