+79 A sequence of positive integers with \(a_1 = 1\) and \(a_9 + a_{10} = 646\) is formed so that the first three terms are in geometric progression, the second, third, and fourth terms are in arithmetic progression, and, in general, for all \(i\ge1\), the terms \(a_{2i - 1}\), \(a_{2i}\), \(a_{2i + 1}\) are in geometric progression, and the terms \(a_{2i}\), \(a_{2i + 1}\), and \(a_{2i + 2}\) are in arithmetic progression. Find the greatest term in this sequence that is less than 1000.
