There is a 1st term and a 2nd term ..... They are asking what is the nth term (the general term).
You are correct but I have to admit that you write it in a very strange way.
I remember when I was a scrub all too well. The answer is 2n or 2 + (n - 1)2 or any else that equals 2n. It is just cleaner to write 2n and certainly much easier to find say the 55 term using 2n then 2 + (n - 1)2
No need to write 2n. If you knew that 2 + 2(n-1) equals 2n then just use 2n as it is easier.
Did you try using it for n=55? You can write any formula you like using any variables of your choice and I will never complain. But you do have to tell me what the variables stand for. Remember I did say what a_n meant. Can you tell me what d represents?
I knew that but I want you to learn that that when you give someone a formula that you define the variable.
The initial form, based on the formula, for the n-th term of the sequence, is indeed the "2 + (n - 1)*2" expression. But then you simplify that down to get 2 + 2n - 2 = 2n + 2 - 2 = 2n + 0 = 2n. The form they're wanting you to give as "the answer" is this simplified form,
You seem to be saying that you do not know what a "sequence" is, to begin with. A "sequence" is any listing of things. A "numeric" sequence is any listing of numbers. To be able to work with a numeric sequence we, of course, have to have some way of know what the sequence is. For example saying "the sequence {a_n} with a_n= n^2" defines a sequence. The formula you give, "a_n= a_1+ (n-1)d" only applies to arithmetic sequences which can also be defined by the recursive formula "a_{n+1}= a_n+ d" where we would also have to be given a_1.