Question

 Q.10

Answer 1

Let 'a' be the first term and 'd' be the common differnce of given A.P. 

Now, 

`t_11=38`

`⇒ a+10d=38 ..................(1)`

`t_16 =73`

`⇒ a+15d=73.....................(2)`

Subtracting (1) from (2), we get 

`5d=35⇒ d=7`

substituting d=7 in (1), we get

`a+10xx7=38`

`⇒a=-32` 

`∴ 31^st " term" =t_31=a+30d=-32+30xx7=-32+210=178`