Since we already know that the sequence is arithmetic, we also know that the difference between consecutive terms is constant. Let's subtract the second term from the first term to get this common difference d.
d=4/7-3/7 ⇔ d= 1/7
Let's now recall the equation for the nth term of an arithmetic sequence.
a_n=a_1+(n-1)d
Next, we can substitute the first term of the sequence 37 and the common difference 17 into the above formula. Let's do it!
To find the common difference, we calculated the difference between the second and the first terms. However, since in an arithmetic sequence the difference between consecutive terms is constant, we can use any two consecutive terms. For example, if we subtract the fourth term from the third term, we get the same common difference.
d=6/7-5/7 ⇔ d= 1/7
