Find the first term and the common difference for the arithmetic sequence for which
a2 = 40 - 3q and a4 = 10p + q.
If p, m, and q form an arithmetic sequence, it can be shown that m = 1 p + q2>2. The number m is the arithmetic mean, or average, of p and q. Given two numbers p and q, if we find k other numbers m1,
m2, c, mk such that
p, m1, m2, c, mk, q
forms an arithmetic sequence, we say that we have "inserted k arithmetic means between p and q."