In simple words you just find what is being added to each term in order to get the next term. Subtracting 17 by 12 you get 5, 22 minus 17 is 5 as well. Now that what is being added is found, you go by the last term given which is 27. You keep adding 5 to the number until you get to the 22nd term which would result in 117. If you would want to know the equation in order for it to be plugged in then you would use f(x)= 7+5x . You would want to use this equation instead of f(x)= 12+5x because putting 1 as x would make it equal to 17 which is NOT the first term but the second.
Suppose you can factorize:
Then by expanding the right side, you have
which means in this case, you have to have
