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Sequences and Series

JEE Main 2026 (Online) 2nd April Evening ShiftMCQMedium📈 Topic in 40% papers+4−1
Ques. 1JEE Main 2026, 2 April (Evening Shift)

Let a1, a2, a3, be an A.P. and g1=a1, g2, g3, be an increasing G.P. If a1=a2+g2=1 and a3+g3=4, then a10+g5 is equal to:

  1. 81
  2. 76
  3. 62
  4. 55

Answer

(4) 55

Solution

a1 = g1 = 1. Let the A.P. have common difference d and the G.P. common ratio q.

a2 + g2 = 1 (1 + d) + q = 1 d = -q

a3 + g3 = 4 (1 + 2d) + q2 = 4

q2 - 2q - 3 = 0 (q - 3)(q + 1) = 0

The G.P. is increasing, q = 3 (not -1), so d = -3.

Then a10 = 1 + 9(-3) = -26 and g5 = 34 = 81, hence

a10 + g5 = -26 + 81 = 55

Answer: (4)

Keep practising — Sequences and Series

Ques. 2JEE Main 2026, 2 April (Evening Shift)

The sum 131+ 13+231+3+ 13+23+331+3+5+ up to 8 terms, is :

  1. 70
  2. 71
  3. 72
  4. 73
Ques. 3JEE Main 2026, 28 January (Morning Shift)

The value of k=1 (-1)k+1 ( k(k+1)k! ) is

  1. e/2
  2. e
  3. 2/e
  4. 1/e
Ques. 4JEE Main 2026, 28 January (Morning Shift)

The common difference of the A.P.: a1, a2, , am is 13 more than the common difference of the A.P.: b1, b2, , bn. If b31 = -277, b43 = -385 and a78 = 327, then a1 is equal to

  1. 21
  2. 19
  3. 24
  4. 16
Ques. 5JEE Main 2026, 28 January (Morning Shift)

In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is R - (a, b), then a2 + b2 is equal to .

Ques. 6JEE Main 2026, 28 January (Evening Shift)

6326 + 10 1325 + 10 2324 + 10 22323 + + 10 2243 is equal to :

  1. 226
  2. 325
  3. 326
  4. 225
Ques. 7JEE Main 2026, 28 January (Evening Shift)

If r=125 ( rr4 + r2 + 1 ) = pq, where p and q are positive integers such that (p, q) = 1, then p + q is equal to .

Ques. 8JEE Main 2026, 24 January (Morning Shift)

Let 729, 81, 9, 1, be a sequence and Pn denote the product of the first n terms of this sequence. If 2 n=140(Pn) 1n = 3 -13 and ( , ) = 1, then + is equal to

  1. 73
  2. 74
  3. 75
  4. 76
Ques. 9JEE Main 2026, 24 January (Morning Shift)

Consider an A.P.: a1, a2, , an; a1 > 0. If a2 - a1 = -34, an = 14a1, and i=1n ai = 5252, then i=117 ai is equal to

  1. 238
  2. 136
  3. 476
  4. 952
Ques. 10JEE Main 2026, 24 January (Evening Shift)

Let a1, a2, a3, a4 be an A.P. of four terms such that each term of the A.P. and its common difference l are integers. If a1 + a2 + a3 + a4 = 48 and a1a2a3a4 + l4 = 361, then the largest term of the A.P. is equal to

  1. 27
  2. 24
  3. 23
  4. 21
Ques. 11JEE Main 2026, 24 January (Evening Shift)

( 13 + 47 ) + ( 132 + 13 47 + 4272 ) + ( 133 + 132 47 + 13 4272 + 4373 ) + up to infinite terms, is equal to

  1. 74
  2. 43
  3. 65
  4. 52

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