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?

40

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.

number of people invited in round 1 = 2

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

total invited = 2 + 4 + ....