题目
Each year, on her birthday, Ananya receives some money from each of her parents.
On Ananya’s first birthday, her father gives her $10. Every subsequent year, her father gives her $5 more than he gave her the previous year.
On Ananya’s first birthday, her mother also gives her $10. Every subsequent year, her mother gives her more than she gave her the previous year.
(a) Show that on Ananya’s eleventh birthday she receives more from her mother than from her father.
(b) Find the total amount of money Ananya receives up to and including her eighteenth birthday.
题目中文翻译
每年生日时，Ananya 都会从父母双方各收到一些钱。
在 Ananya 的第一个生日，她的父亲给她 $10。之后每一年，她的父亲都比前一年多给她 $5。
在 Ananya 的第一个生日，她的母亲也给她 $10。之后每一年，她的母亲都比前一年多给她 。
(a) 证明在 Ananya 的第 11 个生日，她从母亲那里收到的钱比从父亲那里收到的多。
(b) 求 Ananya 到第 18 个生日（含第 18 个生日）为止收到的总金额。
解答
(a)
解法一
思路
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父亲的礼金构成等差数列，母亲的构成等比数列。第十一项相对于首项经过十次递推。
答题过程
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On the eleventh birthday, the father gives dollars. The mother gives dollars. Since , the mother gives more on that birthday.
(b)
解法一
思路
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十八次礼金都要累加。分别求两个数列的前十八项和，最后才把金额舍入到分。
答题过程
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The father’s total is
The mother’s total is . Thus the combined total, to the nearest cent, is $2226.17.