An arithmetic sequence is a sequence where the difference between any two consecutive terms is the same. This difference is called a common difference.
a_2 - a_1 = d a_3 - a_2 = d a_4 - a_3 = d ...
Let's imagine that we know the first term a_1 and the common difference d of an arithmetic sequence. To find the second term of the sequence, we can add the common difference to the first term.
a_2 = a_1 + d
To find the third term, we add the common difference to the second term.
a_3 = a_2 + d ⇒ a_3 = a_1 + 2d
If we repeat that procedure, we will end up with the formula for the nth term of the arithmetic sequence.
a_4 = a_1 + 3d a_5 = a_1 + 4d ... a_n = a_1 + (n-1)d
Now, let's complete the sentence!
