Sequences and Series

Let 3, a, b, c be in A.P. and 3, a-1, b+1, c+9 be in G.P. Then, the arithmetic mean of a, b and c is :

1. -4
2. -1
3. 13
4. 11

Let 3, 7, 11, 15, , 403 and 2, 5, 8, 11, , 404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to .

Let Sn denote the sum of the first n terms of an arithmetic progression. If S10=390 and the ratio of the tenth and the fifth terms is 15:7, then S15-S5 is equal to :

1. 800
2. 890
3. 790
4. 690

If three successive terms of a G.P. with common ratio r(r>1) are the lengths of the sides of a triangle and [r] denotes the greatest integer less than or equal to r, then 3[r]+[-r] is equal to .

The sum of the series 11-3 12+14+ 21-3 22+24+ 31-3 32+34+ up to 10-terms is

1. 45109
2. - 55109
3. 55109
4. - 45109

Let 2nd, 8th and 44th terms of a non-constant A. P. be respectively the 1st, 2nd and 3rd terms of a G. P. If the first term of the A. P. is 1, then the sum of its first 20 terms is equal to -

1. 990
2. 980
3. 960
4. 970

Let Sn denote the sum of first n terms of an arithmetic progression. If S20=790 and S10=145, then S15-S5 is :

1. 405
2. 390
3. 410
4. 395

Let =12+42+82+132+192+262+ upto 10 terms and = n=110 n4. If 4 - =55k+40, then k is equal to .

Let a and b be two distinct positive real numbers. Let 11th term of a GP, whose first term is a and third term is b, is equal to pth term of another GP, whose first term is a and fifth term is b. Then p is equal to

1. 20
2. 24
3. 21
4. 25

Let Sn be the sum to n-terms of an arithmetic progression 3,7,11, . If 40< ( 6n(n+1) k=1n Sk )<42, then n equals .