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Sequences and Series · Question 34

JEE Main 2025 (Online) 7th April Morning ShiftMCQEasy📈 Topic in 42% papers+4−1
1

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.

a - 2, ar - 7, ar2 - 9, ar3 - 5 are in A.P.

From the first three terms: 2(ar - 7) = (a - 2) + (ar2 - 9)

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

From the last three terms: 2(ar2 - 9) = (ar - 7) + (ar3 - 5)

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

(ii) ÷ (i): r = 2, then a = -3

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

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

124(x1 x2 x3 x4) = 518424 = 216

Answer: (2)

JEE Main 2025 (Online) 7th April Morning Shift

Keep practising — Sequences and Series

2

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
JEE Main 2025 (Online) 7th April Evening Shift
3

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
JEE Main 2025 (Online) 7th April Evening Shift
4

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

  1. 40870
  2. 41880
  3. 43890
  4. 33980
JEE Main 2025 (Online) 4th April Morning Shift
5

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
JEE Main 2025 (Online) 4th April Evening Shift
6

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
JEE Main 2025 (Online) 4th April Evening Shift
7

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
JEE Main 2025 (Online) 3rd April Morning Shift
8

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

  1. 7240
  2. 8124
  3. 7130
  4. 6982
JEE Main 2025 (Online) 3rd April Morning Shift
9

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
JEE Main 2025 (Online) 3rd April Evening Shift
10

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
JEE Main 2025 (Online) 2nd April Morning Shift
11

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
JEE Main 2025 (Online) 2nd April Evening Shift

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