solve: `1 + 6 + 11 + 16 +.........+ x = 148`

Explanation

The given series is an arithmetic series in which a=1 and d= ( 6-1) =5
Let is contain n terms, we have to find the nth term.
Now,` S_(n) = 148`
`Rightarrow n/2.[2a + (n-1)d]=148`
`Rightarrown/2.[2xx 1+ ( n-1)xx 5] = 148`
` Rightarrow n(5n-3) = 296 Rightarrow 5n^(2) -3n - 296=0`
` Rightarrow5n^(2) -40n+37n-296=0`
` Rightarrow 5n(n-8) +37 (n-8) =0 Rightarrow (n-8) (5n+37) =0`
`Rightarrown=8 [because n ne(-37)/5]`
` therefore T_(8) =1+(6-1) xx5=36 " " [because T_(n)=a+ (n-1)d]`
Hence, x=36