Sequence and Series Airthmetic and Geometric Progression Part-4

17) A certain ball when dropped to the

      ground rebounds to 4/5th of the height

      from which if falls; it is dropped from a 

      height of 100 meters find the total distance

      it travels before finally coming to rest:

     (a) 600m

     (b) 700m

     (c) 900m

     (d) 200m

18) Find the sum to infinity of the 

       following series:

       1-1+1-1+1-1+...............∞

      (a) 1

      (b) ∞

      (c) 1/2 

      (d) Does not exist      

19) Find n such that  aⁿ⁺¹+ bⁿ⁺¹/  aⁿ +bⁿ

        ^{may be the geometric mean between a}

        ^{and b:}

        ^{(a) 1/2}

        ^{(b) 1}

        ^{(C) -1/2}

        ^{(d) 0}

20)  if x = 1 + (1/3) + (1/3² )+…………………..∞

        y = 1 + (1/4) + (1/4² )+…………………..∞

        Find xy.

       (a) 2

        (b) 1

       (C) 8/9

       (d) 1/2

21) If a,b,c are in A.P. and x,y,z are in G.P.

       then the value of X^{(b – c)} ,y^{(c – a)}  ,z^{(a – b)} is :

      (a) 1

      (b)  0

      (c) b(c - a)

      (d) None