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?

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.