Sequences and Series · Question 33

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

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

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

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

1. 40870
2. 41880
3. 43890
4. 33980

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

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

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

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

1. 7240
2. 8124
3. 7130
4. 6982

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

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