Question

The sums of an terms of two arithmetic progressions are in the ratio (7n – 5) : (5n + 17). Show that their 6^th terms are equal.

Answer 1

Wrong question. It will be 7n + 5 instead of 7n – 5.

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

To Prove: 6^th terms of both AP’S are equal

Let us consider 2 AP series AP₁ and AP₂.

Putting n = 1, 2, 3… we get AP₁ as 12,19,26… and AP₂ as 22,27,32….

So, a₁ = 12, d₁ = 7 and a₂ = 22, d₂ = 5

For AP₁

S₆ = 12 + (6 - 1)7 = 47

For AP₂

S₆ = 22 + (6 - 1)5 = 47

Therefore their 6^th terms are equal.

Hence proved.