Multiple choice

If the sums of n terms of two arithmetic series are in the ratio 2n + 3 : 6n + 5, then the ratio between their 13th terms is

  1. 53 : 155

  2. 27 : 87

  3. 29 : 83

  4. 31 : 89
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A Correct answer
Explanation

If S_n = (2n+3)/(6n+5), the ratio of the n-th terms is given by ratio of S_n / S_m where m = 2n-1. For the 13th term, n=13, so we use the ratio (2(25)+3) / (6(25)+5) = 53 / 155.

AI explanation

The ratio of the sums of n terms of two arithmetic series is given as (2n + 3) : (6n + 5). The ratio of their nth terms is found by replacing n with (2n - 1) in the given sum ratio formula. To find the ratio of the 13th terms, we substitute n = 13 into (2(2n - 1) + 3) : (6(2n - 1) + 5), which simplifies to (4n + 1) : (12n - 1). Substituting n = 13 gives 53 : 155.

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