SEQUENCE & SERIES

1. The ratio of the sums of n terms of two A.P is (7n +1): (4n +27).find the ratio of their 11^th terms.

2. IF a , b, c are in AP. Prove that 1/bc, 1/ac,1/ab are also in AP.

3. If p,q,r are in AP.show that pth,qth,and rth terms of any GP are in GP.

4. Sum the following series up to n terms 7 + 77 + 777 +..........................

5. If b is the GM between a and c P.T (a² + b²) (b² + c²) = (ab + bc) ²

6. Find the sum of the series 12 + 42 + 72 +………...

7. A ball is dropped from a height of 48 m and rebounds two- third of the distance it falls .if it continues to fall and rebounds in this way how far it travels before coming to rest.

8. There are n A.M between 1 and 23 such that the ratio of last mean to the first mean is 7:1. Find the value of n.

9 . If S₁, S₂, S₃ are the sums of first n natural numbers, their squares and their cubes respectively, show that 9 S₂ = S₃ (1 + 8S₁).

10. Find the sum of the series upto n terms

            1³ + 1³+ 2³  + 1³+2³+3³  +…………

         1        1+3           1+3+5

11. If the ratio of the A.M. And G.M. of two nos. a and b be m:n , then find the ratio between the two numbers

PAPER SUBMITTED BY:     PAWAN KUMAR, M.SC (MATHEMATICS), B.ED. , DISM

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