Question

6 people can sit together at 1 rectangular table l. If 2 tables aee placed together, 10 people can sit together. 14 people can sit if three tables are put together. If the pattern countinues how many people could sit together if 100 tables were put together?

Answer 1

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
`=a=6`

Common difference
`=d=10-6=4`

Number of terms=number of table
`=100`

As we know the nth term is given by the formula

`t_n=a+(n-1)d\\ \\ \text{Substitute the values}\\ \\ t_(100)=6+(100-1)*4\\ \\ t_(100)=6+99 *4\\ \\ t_(100)=6+396=402\\`

Hence 402 people can sit.