Question

one bacteria splits into eight bacteria of the next generation. but due to environment, only 50% of one generation can produce next generation. if the seventh generation number is 4096 million, what is the number in the first generation?

Answer 1

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

8(x/2), 8(4x/2), 8(16x/2) . . . . 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

Answer 2

Let x be the no of bacteria in the first generation

2x be the number of bacteria in 2nd generation

3x be the number of bacteria in third generation and so on.

Now

8(x/2), 8(4x/2), 8(16x/2) . . . . And so on.

As x, 4x, 16x, 64x . . . . . it is in GP having common ratio 4.

Hence, 7th term of GP,

x(4)6 = 4096

Or, x = 1 or 1 million.

Ans- 1 million