The first n terms and formulas are: Sn=na 1+n(n- 1)d/2 or Sn=n(a 1+an)/2 (n is a natural number).

A 1 is the first term, an is the last term, n is the number of terms, and d is the tolerance of arithmetic progression.

Geometric series? an=a 1×q^(n- 1)；

sum:sn = a 1( 1-q n)/( 1-q)=(a 1-an×q)/( 1-q)(q≠ 1。

The way to deduce the sum formula of the first n terms of arithmetic progression is to arrange a series in reverse order (reverse order), and then add it to the original series to get n (a 1+an).

Sn？ = A1+A2+A3+...+An

Sn？ =an+ an- 1+an-2......+a 1

Add up and down to get Sn=(a 1+an)n/2.

Extended data:

Square sum correlation formula:

( 1) 1+2+3+.+n=n(n+ 1)/2

(2) 1^2+2^2+3^2+...+n^2=n(n+ 1)(2n+ 1)/6

(3) 1×2+2×3+3×4+4×5+…+n(n+ 1)

=( 1^2+ 1)+(2^2+2)+(3^2+2)+...+(n^2+n)

=( 1^2+2^2+...+n^2)+( 1+2+3+.+n)

= n(n+ 1)(2n+ 1)/6+n(n+ 1)/2

=n(n+ 1)(n+2)