1973 AMC 12 第 26 题
先试着解答 1973 AMC 12 第 26 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1973 AMC 12 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
26.
一个等差数列的项数为偶数。奇数编号各项之和与偶数编号各项之和分别为 与 。若末项比首项大 ，则该等差数列的项数为
The number of terms in an A.P. (Arithmetic Progression) is even. The sums of the odd- and even-numbered terms are and respectively. If the last term exceeds the first by the number of terms in the A.P. is
小提示：
将项数写成 ，公差写成
Write the number of terms as and the common difference as
大提示：
将每个奇数编号项与紧随其后的偶数编号项配对，得到
Pair each odd-numbered term with the following even-numbered term to get
解答：
设数列有 项，公差为 。将每个奇数编号项与后一项配对，可得 末项与首项之差为 因为 ，相减得到 。于是 ，该数列共有 项。
所以正确答案是 E。
Let the progression have terms and common difference Pairing each odd-numbered term with its successor shows that The difference between the last and first terms is Since subtraction gives Hence and the progression has terms.
Therefore, the correct answer is E.
其他年份的第 26 题
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
- 1960 AMC 12
- 1961 AMC 12
- 1962 AMC 12
- 1963 AMC 12
- 1964 AMC 12
- 1965 AMC 12
- 1966 AMC 12
- 1967 AMC 12
- 1968 AMC 12
- 1969 AMC 12
- 1970 AMC 12
- 1971 AMC 12
- 1972 AMC 12
- 1974 AMC 12
- 1975 AMC 12
- 1976 AMC 12
- 1977 AMC 12
- 1978 AMC 12
- 1979 AMC 12
- 1980 AMC 12
- 1981 AMC 12
- 1982 AMC 12
- 1983 AMC 12
- 1984 AMC 12
- 1985 AMC 12
- 1986 AMC 12
- 1987 AMC 12
- 1988 AMC 12
- 1989 AMC 12
- 1990 AMC 12
- 1991 AMC 12
- 1992 AMC 12
- 1993 AMC 12
- 1994 AMC 12
- 1995 AMC 12
- 1996 AMC 12
- 1997 AMC 12
- 1998 AMC 12
- 1999 AMC 12