We notice the common pattern that as you move to the next term, 6 is subtracted.
So, what we want to do is to rewrite the first term in terms of subtracting a multiple of 6.
This way, we can link the term number to the expression.

Term 1 = 56 = 62 - 6 = 62 - 6 × 1
Term 2 = 50 = 62 - 6 - 6 = 62 - 6 × 2
Term 3 = 44 = 62 - 6 - 6 - 6 = 62 - 6 × 3
And so on. Notice that the multiple of 6 is always the same as the term number.
So for the nth term,
Term n = 62 - 6 × n = 62 - 6n
Next,
why is -283 not a term in the sequence?

What we want to do first is to equate -283 to the general term 62 - 6n. We solve for n.
-283 = 62 - 6n
-283 - 62 = -6n
-345 = -6n
n = -345/-6
n = 57.5 (or 57½)
The term numbers are all positive integers (in other words, natural numbers since start from 1st term, then go on to 2nd, 3rd, 4th, 5th,...)
But here we have 57½ which is a mixed number (or 57.5 which is a decimal)
Since these are not positive integerw, -283 is not a term in the sequence.