One bacterium splits into eight bacteria of the next generation. But due to environment, only 50% of one generation can produced the next generation. If the seventh generation number is 4096 million, what is the number in first generation?

Solution (By Examveda Team)

Let the number of bacteria in the 1^st generation be x, then number of bacteria in 2^nd, 3^rd, 4^th . . . . . Generation would be
$$8\left( {\frac{{\text{x}}}{2}} \right),\,8\left( {\frac{{4{\text{x}}}}{2}} \right),\,8\left( {\frac{{16{\text{x}}}}{2}} \right)$$     . . . . And so on.
As x, 4x, 16x, 64x . . . . . it is in GP with common ratio 4
Hence, 7th term of GP,
x(4)⁶ = 4096
or, x = 1 or 1 million.