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# 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?

A. 1 million

B. 2 million

C. 4 million

D. 8 million

E. None of these

### Solution(By Examveda Team)

Let the number of bacteria in the 1st generation be x, then number of bacteria in 2nd, 3rd, 4th . . . . . 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.

1. back solve,
6th year=4096/4=1024.
5th "=1024/4=256.
4th"=256/4=64.
3rd"=64/4=16.
2nd"=16/4=4.
1st"=4/1=1milion.

2. Why you didn't add remaining 50% in the next generation

3. 1/2%= 1/(2*100) = 0.005
{ Explanation: Example-
5% =5/100 so 1/2% = 1/(2*100)}

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