The question is an illustration of arithmetic sequence.
The number of conversation for 19 people is 171
(a) 9 people
[tex]Total = \frac{9 \times 8}{2}[/tex]
9 represents the number of people
8 represents the number of conversation each person had
2 represents the number of people having a conversation at once (i.e 2 people at once)
(b) 19 people
We have:
[tex]n = 19[/tex]
The number of conversation is:
[tex]Total = \frac{n \times (n -1)}{2}[/tex]
So, we have:
[tex]Total = \frac{19 \times (19 -1)}{2}[/tex]
[tex]Total = \frac{19 \times 18}{2}[/tex]
[tex]Total = 19 \times 9[/tex]
[tex]Total = 171[/tex]
Hence, the number of conversation for 19 people is 171
Read more about arithmetic sequence at:
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