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
