It is known that the product of the first three terms of the increasing equal ratio sequence {an} is 512, and the three terms are subtracted by 1, 3 and 9 to form the equal difference sequence. The general term formula of the sequence {an} is obtained

It is known that the product of the first three terms of the increasing equal ratio sequence {an} is 512, and the three terms are subtracted by 1, 3 and 9 to form the equal difference sequence. The general term formula of the sequence {an} is obtained

Let the common ratio of the equal ratio sequence {an} be q, and the product of the first three terms of the equal ratio sequence {an} be 512, ∵ a1a2a3 = a2q · A2 · a2q = (A2) 3 = 512, then the solution is A2 = 8 and ∵ after subtracting 1, 3 and 9 respectively, the three terms form the equal difference sequence, ∵ A1-1, a2-3 and a3-9 form the equal difference sequence, and the result is (A1-1) + (a3-9) = 2 (a2-3), that is, a2q-1 + a2q-9 = 2a2-6, that is, 8q + 8q-10 = 10, then 2q2-5q + 2 = 0, and the solution is q = 2 or q = 12 If ∵ equal ratio sequence {an} is increasing, Q ∵ 1, ∵ q = 2, A1 = a2q = 4, and the general term formula of equal ratio sequence is an = 2n + 1