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Sequences and Series

JEE Main 2025 (Online) 28th January Morning ShiftMCQMedium📈 Topic in 37% papers+4−1
Ques. 1JEE 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

Answer

(2) 3a100 - 100

Solution

2an+2 - 2an+1 = 3an+1 - 3an

an+2 - an+1 = 32(an+1 - an)

So the differences an+1 - an form a G.P. with first term a1 - a0 = 12 and ratio 32.

an = 12 ( 32 )n - 1 32 - 1 = ( 32 )n - 1

k=1100 ak = k=1100 ( 32 )k - 100

= 32 ( 32 )100 - 1 12 - 100

= 3 [ ( 32 )100 - 1 ] - 100

( 32 )100 - 1 = a100

k=1100 ak = 3a100 - 100

Answer: (2)

Keep practising — Sequences and Series

Ques. 2JEE 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. 3JEE 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. 4JEE 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. 5JEE 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. 6JEE 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. 7JEE 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. 8JEE 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
Ques. 9JEE Main 2025, 23 January (Evening Shift)

The roots of the quadratic equation 3x2-px+q=0 are 10th and 11th terms of an arithmetic progression with common difference 32. If the sum of the first 11 terms of this arithmetic progression is 88, then q-2p is equal to .

Ques. 10JEE Main 2025, 22 January (Morning Shift)

Let a1,a2,a3, be a G.P. of increasing positive terms. If a1a5=28 and a2+a4=29, then a6 is equal to:

  1. 812
  2. 784
  3. 628
  4. 526
Ques. 11JEE 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

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