The $n$th term of a sequence is given by $T_n=4n-2$. Verify that the sequence is arithmetic.
I have an answer that says the difference is $4$ and that the sequence is arithmetic but the only difference I get is $0$.
Please explain because I've no idea how to get the $T_n+1$ formula in action with the likes of $n(n+2)$.
Your given that the $n$ th term of sequence is:
$$4n-2=T_n$$
So:
$$4(n+1) -2=T_{n+1}=4n+2$$
Now the difference of the $n+1$ th term and the $n$ th term is:
$$T_{n+1}-T_{n}=(4n+2)-(4n-2)$$
$$=4n+2-4n+2$$
$$=4$$