Difference between revisions of "1960 AHSME Problems/Problem 36"
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Let <math>s_1, s_2, s_3</math> be the respective sums of <math>n, 2n, 3n</math> terms of the same arithmetic progression with <math>a</math> as the first term and <math>d</math> | Let <math>s_1, s_2, s_3</math> be the respective sums of <math>n, 2n, 3n</math> terms of the same arithmetic progression with <math>a</math> as the first term and <math>d</math> | ||
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==See Also== | ==See Also== | ||
{{AHSME 40p box|year=1960|num-b=35|num-a=37}} | {{AHSME 40p box|year=1960|num-b=35|num-a=37}} | ||
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+ | [[Category:Introductory Algebra Problems]] |
Latest revision as of 19:20, 17 May 2018
Problem
Let be the respective sums of terms of the same arithmetic progression with as the first term and as the common difference. Let . Then is dependent on:
Solution
The nth term of the sequence with first term is . That means the sum of the first terms is with first term is .
The 2nth term of the sequence with first term is . That means the sum of the first terms is with first term is .
The 3nth term of the sequence with first term is . That means the sum of the first terms is with first term is .
Substituting , , and with its respective values results in
The answer is .
See Also
1960 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 35 |
Followed by Problem 37 | |
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All AHSME Problems and Solutions |