等差数列中前n项的和为210,其中前四项的和为40,后四项的和为80,则n的值等于

Question

等差数列中前n项的和为210,其中前四项的和为40,后四项的和为80,则n的值等于

Answer 1

设数列为 a1,a2,...,an-1,an
now:a1+a2+a3+a4+an-3+an-2+an-1+an = 40+80 = 120
又有 a1+an = a2+an-1 = a3+an-2 = a4+an-3
so:a1+an = 120/4 = 30
而 前n项和公式 为 210 = （a1+an）n/2
= 30n/2 = 15n
n = 14