Solution:
we are given that
6 people can sit together at 1 rectangular table.
2 tables are placed together, 10 people can sit together.
14 people can sit if three tables are put together.
It mean we get a sequence
6,10,14..........
So its making an arithmetic progression, where
First term[tex]=a=6[/tex]
Common difference[tex]=d=10-6=4[/tex]
Number of terms=number of table[tex]=100[/tex]
As we know the nth term is given by the formula
[tex]t_n=a+(n-1)d\\
\\
\text{Substitute the values}\\
\\
t_{100}=6+(100-1)\times4\\
\\
t_{100}=6+99 \times4\\
\\
t_{100}=6+396=402\\[/tex]
Hence 402 people can sit.
