(b) The average weight of eggs of first generation is k gm and the no. of eggs is ânâ.
Let
a1,a2,a3...,an be the weights of n eggs of the first generation
â´
k= â´
nk=z1+z2+z3+..+znââââââ ...1
where
z1is the average weight of its ânâ child eggs,
z2is the average weight of its own ânâ child eggs and so on. Child egg is referred to the egg of next generation produced by its mother eggs.
â´
z1= z2= z3= etc.
Substituting the values of
z1+z2+z3...in 1
â Therefore,
n2k is the total weight of all the eggs of second generation.
Similarly, each of
a1,b1,c1,a2,b2,c2.... are the average weights of n eggs of their child eggs. Hence in the third generation total weight will be
n3k. Thus the total weight of all the eggs of
rth generation is
nrk