Given that A1 = 1 in the sequence {an}, the point (an, an + 1) is on the image of function y = 3x + 2 (n ∈ n *) (I) prove that the sequence {an + 1} is an equal ratio sequence; (II) find the sum of the first n terms of the sequence {an}

Given that A1 = 1 in the sequence {an}, the point (an, an + 1) is on the image of function y = 3x + 2 (n ∈ n *) (I) prove that the sequence {an + 1} is an equal ratio sequence; (II) find the sum of the first n terms of the sequence {an}

It is proved that: (I) from the meaning of the question, an + 1 = 3an + 2, then an + 1 + 1 = 3 (an + 1) and a1 + 1 = 2 ｛ sequence {an + 1} is an equal ratio sequence with 2 as the first term and 3 as the common ratio. (II) from (I), an + 1 = 2.3n − 1 ｛ an = 2.3n − 1 ｛ Sn = (2.30 − 1) + (2.3 − 1) + +(2•3n−1−1)=2（1+3+… +3n-1）-n=2•1−3n1−3−n=3n-1-n