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

Explanation

The given arithmetic
sequence is `1+6+11+16+....+x` in which the first term is `a_1` `=1`, second term is `a _2​` `=6`, nth term is `T_n​` =x and the sum of the series is `S_n`​ `=148`.

We find the common difference d by subtracting the first term from the second term as shown below:

d=`a_2`​−`a_1​` `=6−1=5`

We know that the general term of an arithmetic
progression with first term a and common difference d is `T_n``=a+(n−1)d`, therefore, with a=1,d=5 and `T_n`​ `=x`, we have

`T_n`` =a+(n−1)d`

`=>x=1+(n−1)5`
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