The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.

Question

Philoid · Accepted Answer

Let a₁, a₂, and d₁, d₂ be the first terms and the common difference of the first and second arithmetic progression respectively.

Given,

⇒

Putting n = 35 in the above equation

⇒

∴

Thus, the ratio of 18^th term of both the A.P.s is 179: 321