Sequences and Series

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

The number of common terms in the progressions 4, 9, 14, 19, , up to 25th term and 3, 6, 9, 12, , up to 37th term is :

1. 9
2. 8
3. 5
4. 7

If 8=3+ 14(3+p)+ 142(3+2p)+ 143(3+3p)+ , then the value of p is .

The 20th term from the end of the progression 20, 19 14, 18 12, 17 34, , -129 14 is :

1. -115
2. -100
3. -110
4. -118