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

Answer:

Number of people chosen in the sixth round is 729                  

Step-by-step 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

$a_n=ar^{n-1}$

$a_6=3\times3^{6-1}$

$a_6=3\times3^{5}$

$a_6=3^6=729$

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

Answer 2

In the sixth round 729 people are chosen.