High school series problem, prove your IQ! The sum of the first n terms of {an} is Sn, an ≠ 0, a 1 is a constant, and - a 1, Sn and an + 1 form an arithmetic sequence 1. Find the general formula of {an} 2. Let BN = 1-sn, ask whether there is A1, make the sequence {BN} equal ratio sequence. If there is, find the value of A1, if not, explain the reason

High school series problem, prove your IQ! The sum of the first n terms of {an} is Sn, an ≠ 0, a 1 is a constant, and - a 1, Sn and an + 1 form an arithmetic sequence 1. Find the general formula of {an} 2. Let BN = 1-sn, ask whether there is A1, make the sequence {BN} equal ratio sequence. If there is, find the value of A1, if not, explain the reason

1. The results are as follows: 1
2Sn-1=-a1+an
By subtracting the two formulas, 2An = an + 1-an
So, 3an = an + 1
So, {an} is an equal ratio sequence
Among them, the prime minister is - A1, and the common ratio is 3
So, an = - A1 × 3 ^ n-1
2、bn=1-Sn=1-（-a1+an+1）/2=1-（-a1-a1×3^n）/2=(2+a1+a1×3^n)/2
When A1 = - 2, {BN} is an equal ratio sequence