若Sn是等差数列{an}的前n项和,且S10-S5=20,则S15的值为
人气：261 ℃ 时间：2020-04-07 08:03:33
解答
a(n) = a + (n-1)d.
s(n) = na + n(n-1)d/2.
20 = s(10) - s(5) = 10a + 10*9d/2 - 5a - 5*4d/2 = 5a + 5*7d,
s(15) = 15a + 15*14d/2 = 15(a + 7d) = 3[5a + 5*7d] = 3*20 =60
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