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

assuming first AP whose first term is a and common difference d

To find: the ratio of 18^th term of a given AP

we know that the sum of AP is given by the formula:

Substituting the values in the above equation

assuming second AP whose first term is A and common difference D

we know that the sum of AP is given by the formula:

substituting the values in the above equation

…. (i)

Given the ratio of the 18^th term is required of both AP’s which is

Substituting n = 35 in (i) we get