等差数列Ⅱ在等差数列an中am+m=A,am-n=B（m>n)则am等于几多?an等于几多?

Question

等差数列Ⅱ
在等差数列【an】中am+m=A,am-n=B（m>n)则am等于几多?an等于几多?

Answer 1

a(m+n)=a1+(m+n-1)*d=A (1)
a(m-n)=a1+(m-n-1)*d=B (2)
(1)-(2)得:
d=(A-B)/2n
a1=A-(m+n-1)*(A-B)/2n
am=a1+(m-1)*d
=A-(m-1)*(m+n-1)*(A-B)/2n
an=a1+(n-1)*d
=A-(n-1)*(m+n-1)*(A-B)/2n
答案需要你自己再化简一下