UC知道a-level数学
来源：百度知道 编辑：UC知道 时间：2024/05/05 14:12:04
A girl saves money over a period of 200 weeks. She saves 5p in Week 1, 7p in Week 2,
9p in Week 3, and so on until Week 200. Her weekly savings form an arithmetic
sequence.
(a) Find the amount she saves in Week 200.
(b) Calculate her total savings over the complete 200 week period.
9p in Week 3, and so on until Week 200. Her weekly savings form an arithmetic
sequence.
(a) Find the amount she saves in Week 200.
(b) Calculate her total savings over the complete 200 week period.
这是个等差数列，首项为5，公差为2 其通项公式为w=x+(n-1)d首项x，公差d，代入得w=2n+3 n=200, w=403 第二是求等差数列的前n项和问题.s=(x+w)n/2即首项加末项乘项数的一半.(5+403)*200/2=4080
第一周5，第二周7，第三周9，第n周是 2n+3
(a)
403
(b)
5 + 7 + 9 + ... + 203
= 200 * 3 + 2 * (1 + 2 + 3 + ... + 200)
= 200 * 3 + 200 * 201
= 40800