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Sequences and Series

JEE Main 2025 (Online) 22nd January Morning ShiftMCQMedium📈 Topic in 22% papers+4−1
Ques. 1JEE Main 2025, 22 January (Morning Shift)

If r=1nTr= (2n-1)(2n+1)(2n+3)(2n+5)64, then n r=1n ( 1Tr ) is equal to :

  1. 23
  2. 13
  3. 1
  4. 0

Answer

(1) 23

Solution

Tn=Sn-Sn-1= (2n-1)(2n+1)(2n+3)8

1Tr=2 [ 1(2r-1)(2r+1)- 1(2r+1)(2r+3) ] (telescopes)

r=1n 1Tr=2 [ 13- 1(2n+1)(2n+3) ]

As n : 23

Answer: (1)

Keep practising — Sequences and Series

Ques. 2JEE Main 2025, 22 January (Evening Shift)

Suppose that the number of terms in an A.P. is 2k, k . If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27, then k is equal to:

  1. 8
  2. 6
  3. 4
  4. 5
Ques. 3JEE Main 2024, 9 April (Morning Shift)

If the sum of the series 11 (1 + d) + 1(1 + d)(1 + 2d) + + 1(1 + 9d)(1 + 10d) is equal to 5, then 50d is equal to :

  1. 5
  2. 10
  3. 15
  4. 20
Ques. 4JEE Main 2024, 9 April (Evening Shift)

Let a, ar, ar2, be an infinite G.P. If n=0 arn = 57 and n=0 a3r3n = 9747, then a + 18r is equal to

  1. 27
  2. 38
  3. 31
  4. 46
Ques. 5JEE Main 2024, 9 April (Evening Shift)

If ( 1 + 1 + 1 + 2 + + 1 + 1012 ) - ( 12 1 + 14 3 + 16 5 + + 12024 2023 ) = 12024, then is equal to .

Ques. 6JEE Main 2024, 8 April (Morning Shift)

Let the positive integers be written in the form : [figure] If the kth row contains exactly k numbers for every natural number k, then the row in which the number 5310 will be, is .

Ques. 7JEE Main 2024, 8 April (Evening Shift)

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 703 and the product of the third and fifth terms is 49. Then the sum of the 4th, 6th and 8th terms is equal to:

  1. 78
  2. 96
  3. 91
  4. 84
Ques. 8JEE Main 2024, 8 April (Evening Shift)

An arithmetic progression is written in the following way [figure] The sum of all the terms of the 10th row is .

Ques. 9JEE Main 2024, 6 April (Morning Shift)

Let the first term of a series be T1 = 6 and its rth term Tr = 3Tr-1 + 6r, r = 2, 3, , n. If the sum of the first n terms of this series is 15 (n2 - 12n + 39 ) (4 6n - 5 3n + 1 ), then n is equal to .

Ques. 10JEE Main 2024, 6 April (Evening Shift)

n (12 - 1)(n - 1) + (22 - 2)(n - 2) + + ((n - 1)2 - (n - 1)) 1(13 + 23 + + n3) - (12 + 22 + + n2) is equal to :

  1. 23
  2. 12
  3. 34
  4. 13
Ques. 11JEE Main 2024, 6 April (Evening Shift)

Let ABC be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle ABC and the same process is repeated infinitely many times. If P is the sum of perimeters and Q is the sum of areas of all the triangles formed in this process, then :

  1. P2 = 72 3Q
  2. P2 = 36 3Q
  3. P = 36 3Q2
  4. P2 = 6 3Q

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