SEQUENCES AND SERIES

1. If are in A.P, then a+b,
   b+c, c+a are in
   (a) AP (b) GP (c) HP (d) None


2. If ratio of sum of ‘n’ terms of
   two AP’s are ( ) ( ),
   find ratio of their 11th terms
   (a) 2:3 (b) 3:4 (c) 4:3 (d) 5:6


3. If , β are roots of equation

of equation -
12x+b=0 and , β, are in G.P,
then (a, b) is
(a) (3, 12) (b) (12, 3) (c) (2, 32)
(d) (4, 16)

4. If x, 2x+2. 3x+3 are in GP, then
   find 4th term
   (a) 27 (b) -27 (c) 13.5 (d) -13.5


5. The value of ⁄^ ⁄^
   ⁄^ ............................
   (a) (b) (c) 3 (d)


6. If a, b, c are in A.P, then

are in
(a) AP (b) GP (c) HP (d) None

7. The sum of 24 terms of

following series √ (^) √ (^) √
√^ +........^
(a) 300 (b) 300√ (c) 200√ (d)
200

8. The sum up to ‘n’ terms of
   following series
   1+3+7+15+31+........
   (a) - n (b) - n-2 (c) - n-
   2 (d) None


9. If a, b, c are in A.P, then ,
   are in
   (a) A.P (b) GP (c) HP (d) None


10. If a, b, c are in AP, and
    x= 1+a+ .......
    y= 1+b+ +.........
    z= 1+c+ +..........
    then x, y, z are in
    (a) AP (b) GP (c) HP (d) None


11. If = nP+^ (^ ) is
    for AP, find common difference
    (a) P+ (b) 2P+3 (c) 2 (d)


12. If x>1, y>1, z>1 are in GP, then

,

,

are in^

(a) AP (b) GP (c) HP (d) None

13. If n!, 3×(n!), (n+1)n! are in GP,
    find n
    (a) 3 (b) 4 (c) 8 (d) 10


14. If for an AP, and
    then is
    (a) (b) (c) 1 (d) 0