Find the sum of the first $75$ terms of the arithmetic sequence that starts $5, 8, 11, ldots$

Find the sum of the first $75$ terms of the arithmetic sequence that starts $5, 8, 11, \ldots$

The answer is $8700$.

I found a formula to be $3x+2$.
So the $1$st term is
$$3(1)+2=5$$
2nd term
$$3(2)+2=8$$
3rd term
$$3(3)+2=11$$

And so on to the 75th term
$$3(75)+2=227$$
I did not get the right answer? What did I do wrong? Please help?

Answer

$$u_1=5$$
$$u_2=8=5+3$$
$$u_3=11=5+2.3$$
$$u_{75}=5+74.3=227$$

$$S=5+8+11+...+224+227$$

$$S=227+224+...8+5$$
by sum
$$2S=232+232+...232=232.75$$

$$S=116.75=8700$$