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安那蘇姆您好，我是收到電郵求救過來的。

等差數列a1, a2, a3, ..., an 中,若 a50 - a20 = 15, 則 a300 - a100 值 = ?

答案是100

請問詳細算法過程?

令 a 為首項, d 為 公差。
an = a + (n-1)d

a50 = a + 49d
a20 = a + 19d

兩者相減得 a50 - a20 = 30d = 15
即 d = 1/2

a300 = a + 299d
a100 = a + 99d

兩者相減得 a300 - a100 = 200d = 200 * 1/2 = 100

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

求級數10+11-12+13-14+15-16+17-18+....中, 前101項總合?

答案是-40

請問詳細算法過程?

除首項外，其餘兩個兩個為一組。

10 + (11 - 12) + (13 - 14) + (15 - 16) + ... + 至 第101項

= 10 + (-1) + (-1) + ... + (-1)  這裏 (-1) 共有 (101 - 1)/2 = 50 項

= 10 + (-1)*50

= 10 - 50

= -40
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

如果不明白可以補充發問。

努力！

祝好運！

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