Given the sequence an satisfies a1 + 3a2 + 3 & # 178; A3 +... + 3 (n-1) an = n & # 178;, find the general term formula of an Is n-1 power of 3

Given the sequence an satisfies a1 + 3a2 + 3 & # 178; A3 +... + 3 (n-1) an = n & # 178;, find the general term formula of an Is n-1 power of 3

a1+3a1+3²a2+… +3^(n-2)a(n-1)+3^(n-1)an=n²
When n = 1, A1 = 1;
When n ≥ 2, a1 + 3A1 + 3 and # 178; A2 + +3^(n-2)a(n-1)=(n-1)²
By subtracting the two formulas, we get: 3 ^ (n-1) an = n & # 178; - (n-1) &# 178; = 2N-1
So an = (2n-1) / 3 ^ (n-1) (n ≥ 2)
When n = 1, A1 = (2-1) / 1 = 1
So an = (2n-1) / 3 ^ (n-1) (n ∈ n +)

Given the positive term sequence {an}, the first n terms and Sn satisfy 10sn = an2 + 5An + 6, and A1, A3, A15 are equal proportion sequence, find the general term an of the sequence {an}

∵ 10sn = an2 + 5An + 6, ① ∵ 10A1 = A12 + 5A1 + 6, the solution is A1 = 2 or A1 = 3. And 10sn-1 = an-12 + 5an-1 + 6 (n ≥ 2), ② from ① - ②, we get & nbsp; 10An = (an2-an-12) + 5 (an-an-1), that is, (an + an-1) (an-an-1-5) = 0 ∵ an + an-1 > 0, ∵ an-an-an-1 = 5 & nbsp; (n ∵

What are the common methods to summarize the high school mathematics sequence?
What else can I do besides subtraction

1: Direct legal
2: Summation of union terms
3: Sum of split terms
4: Split item reorganization method
5: Offset subtraction
6: Addition in reverse order
7: Inductive conjecture