Question

Two friends share a secret on the first day. The second date they each till one another different friend, so now for people know the secret. On day three or four till a different person, now ate know the secret. The secret keeps growing in this week. On what day will the number who know the secret past 1 million

Answer 1

The 20th day

Explanation:

On the first day, number of people who know the secret=2

Number of people On the second day =2X2=4

Number of people On the third day =4X2=8

We can see that on each passing day, the number keeps doubling.

This is an example of a geometric progression.

Now we are to determine the number of days when the number of people who know the secret will grow past 1,000,000

For the G.P. 2,4,8,...

a=2, common ratio, r= 2

Uₙ=arⁿ⁻¹

arⁿ⁻¹>1000000

2X2ⁿ⁻¹>1000000

2ⁿ⁻¹⁺¹>1000000

2ⁿ>1000000<2²⁰=1048576

2ⁿ<2²⁰

n<20

It means on the 20th day, more than 1 million people will have been told the secret