Hi there! Thank you for the opportunity to help you with your question!
In an arithmetic series, we have evenly spaced terms (that is, we difference between consecutive terms is constant).
(For example, 4, 7, 10, 13, 16, 19 ... is an arithmetic sequence.)
More generically, if the first term of the sequence is a1, then the second will be
a2 = a1 + d
a3 = a2 + d = a1 + 2d
a4 = a3 + d = a1 + 3d...
and so on
In this problem, we know that the 10th number is 3.
a10 = 3
But we also know from the discussion above that
a10 = a1 + 9d.
So a1 +9d = 3
Now, we need to use the second piece of information, that the sum of the first six terms (S6) is equal to 76.5. Now, how can we write the sum of the first six terms of this series? We could do it explicitly: