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If the sums of the first n terms of two arithmetic progressions are in the ratio (2n + 3): (6n + 5), then what is the ratio of their 13th terms?

1. 53: 155
2. 27: 87
3. 29: 83
4. 31: 89

Correct answer: 53: 155

Solution

The ratio of the m-th terms equals the sum ratio evaluated at n = 2m-1. For m = 13, n = 25: (2*25+3)/(6*25+5) = 53/155.

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