Sequences and Series

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 .

If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to

1. 7
2. 6
3. 5
4. 4

If e a, e b, e c are in an A.P. and e a- e 2b, e 2b- e 3c, e 3c- e a are also in an A.P., then a:b:c is equal to

1. 6:3:2
2. 9:6:4
3. 25:10:4
4. 16:4:1

If each term of a geometric progression a1, a2, a3, with a1= 18 and a2 a1, is the arithmetic mean of the next two terms and Sn=a1+a2+ +an, then S20-S18 is equal to

1. -215
2. 215
3. -218
4. 218