If the ratio between the sums of n terms of two arithmetic progressions is (7n + 1) : (4n + 27), find the ratio of their 11 th terms.

Question

Philoid · Accepted Answer

Given: Ratio of sum of n^th terms of 2 AP’s

To Find: Ratio of their 11^th terms

Let us consider 2 AP series AP₁ and AP₂.

Putting n = 1, 2, 3… we get AP₁ as 8, 15 22… and AP₂ as 31, 35, 39….

So, a_{1 =} 8, d_{1 =} 7 and a_{2 =} 31, d_{2 =} 4

For AP₁

S₆ = 8 + (11 - 1)7 = 87

For AP₂

S₆ = 31 + (11 - 1)4 = 81

Required ratio =