General term formula

an=a 1+(n- 1)d

an = Sn-S(n- 1)(n & gt； =2)

Sum of the first n terms

sn = n(a 1+an)/2 = n * a 1+n(n- 1)d/2

2. Equal ratio series

General term formula

an=a 1q^(n- 1)

an = Sn/S(n- 1)(n & gt； =2)

Sum of the first n terms

When q≠ 1, the formula of the sum of the first n terms of the geometric series is

sn=a 1( 1-q^n)/( 1-q)=(a 1-an*q)/( 1-q)(q≠ 1)

3. Fibonacci series

General term formula

an=( 1/√5)*{[( 1+√5)/2]^n-[( 1-√5)/2]^n}

Sum of the first n terms

sn =( 1/√5)*[( 1+√5)/2 )^(n+2)-[(( 1-√5)/2 )^(n+2)]- 1

4. Dayan series

General term formula

an=(n^2- 1)/2(n = 2k- 1，k∈N)

an=n^2/2 (n=2k，k∈N)

Sum of the first n terms

sn =(N- 1)(N+ 1)(2n+3)/ 12(N = 2k- 1，k∈N)

sn = N(N+2)(2n- 1)/ 12(N = 2k，k∈N)