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Sequences and Series

JEE Main 2025 (Online) 29th January Morning ShiftMCQEasy📈 Topic in 58% papers+4−1
Ques. 1JEE Main 2025, 29 January (Morning Shift)

Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its 11th term is :

  1. 108
  2. 90
  3. 122
  4. 84

Answer

(2) 90

Solution

Let first term = a, common difference = d.

a + (a + d) + (a + 2d) = 54 a + d = 18

S20 = 10(2a + 19d) = 10(36 + 17d)

1600 < 360 + 170d < 1800

1240 < 170d < 1440

7.29 < d < 8.47

d is an integer d = 8, a = 10

T11 = a + 10d = 10 + 80 = 90

Answer: (2)

Keep practising — Sequences and Series

Ques. 2JEE Main 2025, 29 January (Morning Shift)

The value of n ( k=1n k3 + 6k2 + 11k + 5(k+3)! ) is :

  1. 5/3
  2. 2
  3. 4/3
  4. 7/3
Ques. 3JEE Main 2025, 29 January (Evening Shift)

Let a1,a2, ,a2024 be an Arithmetic Progression such that a1+(a5+a10+a15+ +a2020)+a2024=2233. Then a1+a2+a3+ +a2024 is equal to .

Ques. 4JEE Main 2025, 28 January (Morning Shift)

Let an be a sequence such that a0 = 0, a1 = 12 and 2an+2 = 5an+1 - 3an, n = 0, 1, 2, 3, . Then k=1100 ak is equal to

  1. 3a100 + 100
  2. 3a100 - 100
  3. 3a99 - 100
  4. 3a99 + 100
Ques. 5JEE Main 2025, 28 January (Morning Shift)

Let Tr be the rth term of an A.P. If for some m, Tm = 125, T25 = 120, and 20 r=125Tr = 13, then 5m r=m2mTr is equal to

  1. 98
  2. 126
  3. 112
  4. 142
Ques. 6JEE Main 2025, 28 January (Evening Shift)

For positive integers n, if 4an = (n2 + 5n + 6 ) and Sn = k=1n ( 1ak ), then the value of 507S2025 is :

  1. 540
  2. 675
  3. 1350
  4. 135
Ques. 7JEE Main 2025, 28 January (Evening Shift)

The interior angles of a polygon with n sides are in an A.P. with common difference 6 . If the largest interior angle of the polygon is 219 , then n is equal to .

Ques. 8JEE Main 2025, 24 January (Morning Shift)

Let Sn= 12+ 16+ 112+ 120+ upto n terms. If the sum of the first six terms of an A.P. with first term -p and common difference p is 2026 S2025, then the absolute difference between 20th and 15th terms of the A.P. is

  1. 20
  2. 45
  3. 90
  4. 25
Ques. 9JEE Main 2025, 24 January (Evening Shift)

In an arithmetic progression, if S40=1030 and S12=57, then S30-S10 is equal to :

  1. 525
  2. 505
  3. 510
  4. 515
Ques. 10JEE Main 2025, 24 January (Evening Shift)

If 7=5+ 17(5+ )+ 172(5+2 )+ 173(5+3 )+ , then the value of is :

  1. 17
  2. 1
  3. 67
  4. 6
Ques. 11JEE Main 2025, 23 January (Morning Shift)

If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

  1. -120
  2. -1200
  3. -1080
  4. -1020

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