1973 AMC 12 Problem 26
Attempt Problem 26 of the 1973 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1973 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
26.
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
Answer: E
Small hint:
Write the number of terms as and the common difference as
Big hint:
Pair each odd-numbered term with the following even-numbered term to get
Solution:
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.
Problem 26 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
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- 1954 AMC 12
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