Question

满足首项加上末项乘以项数除以2的数列求和公式的数列一定是等差数列

Answer 1

Sn=(A1+An)*n/2

An = Sn -Sn-1 =(A1+An)*(n)/2-(A1+An-1)*(n-1)/2

=( A1+nAn-(n-1)An-1 )/2

移项得 An=A1+(n-1)(An-An-1) (1)

An-1=A1+(n-2)(An-1-An-2) (2)

(1)-(2) 化简得

An-An-1＝An-1-An-2 是等差数列