Question

For a game, three people are chosen in the first round. Each of those three people chooses 3 people in the second round. How many are chosen the sixth round.

Answer 1

In the sixth round 729 people are chosen.

Answer 2

Number of people chosen in the sixth round is 729

Explanation:

Given : For a game - 3 people are chosen in first round then each of three chooses 3 people in the second round ans so on.

To find : How many are chosen the sixth round.

Solution : We know,

In first round 3 people choose ⇒no. of people =3

In second round 3 people individually choose 3 people ⇒no. of people = 9

since the number of people chosen with a constant amount forming a geometric series

Geometric series - A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed also called as common ratio.

General form:
`a,ar,ar^2,ar^3......`

and n-th term of geometric series is
`a_n=ar^(n-1)`

where a - first term , r- common ratio and n-number of term

For the sixth round - a=3, r=3 , n=6

`a_n=ar^(n-1)`

`a_6=3*3^(6-1)`

`a_6=3*3^(5)`

`a_6=3^6=729`

Therefore, number of people chosen in the sixth round is 729