Question

You are having a pool party and invite 2 of your best friends. These two friends each invite two other people. Each of these 2 people invite 2 people that haven't been invited. How many people will be invited if this process continues for four rounds?

Answer 1

number of people invited in round 1 = 2

number of people invited in round 2 = 4
.....

total invited = 2 + 4 + ....

Answer 2

40

Answer 3

[AI-generated answer — Explain Bot]

To solve this problem, we can think about it in terms of a sequence and use the power of exponents to calculate the number of people at each round.

In the beginning, there are 2 friends you invited, so there are 2 people in the first round.

In the second round, each of your friends invites 2 people, so the total number of people is 2 friends × 2 new people = 4 people in the second round.

In the third round, each of the 4 new people from the second round invites another 2 people, so the total number of people is 4 new people × 2 new people = 8 people in the third round.

Finally, in the fourth round, each of the 8 new people from the third round invites yet another 2 people, so the total number of people is 8 new people × 2 new people = 16 people in the fourth round.

Therefore, if this process continues for four rounds, there will be a total of 2 + 4 + 8 + 16 = 30 people invited.