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Sequences and Series

JEE Main 2025 (Online) 7th April Morning ShiftMCQQualifier📈 Topic in 40% papers+4−1
Ques. 1JEE Main 2025, 7 April (Morning Shift)

Let x1, x2, x3, x4 be in a geometric progression. If 2, 7, 9, 5 are subtracted respectively from x1, x2, x3, x4, then the resulting numbers are in an arithmetic progression. Then the value of 124(x1 x2 x3 x4) is:

  1. 18
  2. 216
  3. 36
  4. 72

Answer

(2) 216

Solution

Let x1 = a, x2 = ar, x3 = ar2, x4 = ar3. Since a - 2, ar - 7, ar2 - 9, ar3 - 5 are in A.P., the first three terms give

2(ar - 7) = (a - 2) + (ar2 - 9)

a(r2 - 2r + 1) = -3 a(r-1)2 = -3 ... (i)

and the last three terms give

2(ar2 - 9) = (ar - 7) + (ar3 - 5)

ar(r2 - 2r + 1) = -6 ar(r-1)2 = -6 ... (ii)

Dividing (ii) by (i), r = 2, and then a = -3.

So the G.P. is -3, -6, -12, -24 (check: -5, -13, -21, -29 is an A.P. ✓), and

x1 x2 x3 x4 = (-3)(-6)(-12)(-24) = 5184

124(x1 x2 x3 x4) = 518424 = 216

Answer: (2)

Keep practising — Sequences and Series

Ques. 2JEE Main 2025, 7 April (Evening Shift)

Let an be the nth term of an A.P. If Sn = a1 + a2 + a3 + + an = 700, a6 = 7 and S7 = 7, then an is equal to :

  1. 65
  2. 56
  3. 70
  4. 64
Ques. 3JEE Main 2025, 7 April (Evening Shift)

If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15309, then the sum of its first nine terms is :

  1. 757
  2. 755
  3. 750
  4. 760
Ques. 4JEE Main 2025, 4 April (Morning Shift)

1 + 3 + 52 + 7 + 92 + up to 40 terms is equal to

  1. 40870
  2. 41880
  3. 43890
  4. 33980
Ques. 5JEE Main 2025, 4 April (Evening Shift)

If the sum of the first 20 terms of the series 4 14 + 3 12 + 14 + 4 24 + 3 22 + 24 + 4 34 + 3 32 + 34 + 4 44 + 3 42 + 44 + is mn, where m and n are coprime, then m + n is equal to :

  1. 423
  2. 421
  3. 422
  4. 420
Ques. 6JEE Main 2025, 4 April (Evening Shift)

Consider two sets A and B, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the elements of B be 36 and q respectively. Let d and D be the common differences of A.P.'s in A and B respectively such that D=d+3, d>0. If p+qp-q= 195, then p-q is equal to

  1. 540
  2. 450
  3. 600
  4. 630
Ques. 7JEE Main 2025, 3 April (Morning Shift)

Let a1, a2, a3, be a G.P. of increasing positive numbers. If a3 a5 = 729 and a2 + a4 = 1114, then 24(a1 + a2 + a3) is equal to

  1. 128
  2. 129
  3. 131
  4. 130
Ques. 8JEE Main 2025, 3 April (Morning Shift)

The sum 1 + 3 + 11 + 25 + 45 + 71 + upto 20 terms, is equal to

  1. 7240
  2. 8124
  3. 7130
  4. 6982
Ques. 9JEE Main 2025, 3 April (Evening Shift)

The sum 1 + 1 + 32! + 1 + 3 + 53! + 1 + 3 + 5 + 74! + up to terms, is equal to

  1. 3e
  2. 2e
  3. 4e
  4. 6e
Ques. 10JEE Main 2025, 2 April (Morning Shift)

Let a1, a2, a3, be in an A.P. such that k=112 a2k-1 = - 725a1, a1 0. If k=1n ak = 0, then n is :

  1. 18
  2. 17
  3. 11
  4. 10
Ques. 11JEE Main 2025, 2 April (Evening Shift)

The number of terms of an A.P. is even; the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term exceeds the first by 212. Then the number of terms which are integers in the A.P. is :

  1. 6
  2. 4
  3. 8
  4. 10

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