General formula: an = a1+(n-1) d;

Sum formula1:sn = a1n+n (n-1) d/2;

Sum formula 2: sn = n (a1+an)/2;

Intermediate formula: if m+n = 2k; m，N，k∈N； Then for arithmetic progression: 2ak = am+an;

Equation formula: if m+n = p+q; M, n, p, q∈N, then for arithmetic progression: am+an = AP+AQ;

Geometric series:

General formula: an = a1q (n-1);

Sum formula1:sn = a1(1-q n)/(1-q) (q ≠1);

Sum formula 2: Sn = (a1-anq)/(1-q) (q ≠1);

Intermediate formula: if m+n = 2k; m，N，k∈N； For geometric series, there are: (ak)? = am * an

Equation formula: if m+n = p+q; M, n, p, q∈N, then for arithmetic progression: am * an = AP * AQ；;

Commonly used when solving problems:

When n= 1, a 1=s 1=?

When n≥2, an=Sn-S(n- 1)=?

When you can't solve the general formula, try to turn the given known conditions into geometric series or arithmetic progression; Also, using the first few terms (such as a 1, a2, a3), guess the general term formula of the sequence, and then prove it by mathematical induction; The steps of mathematical induction are as follows: step one, when n= 1, it holds; The second step is to assume that n=k is true and prove that n=k+ 1

References:

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