If the sum of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6, find the ratio of their 18^th terms.

Question

If the sum of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6, find the ratio of their 18th terms.

Philoid · Accepted Answer

For first A.P. :

Let first term = a1

Common difference = d1

and Sn1 = Sum of n terms

For second A.P. :

Let first term = a2

Common difference = d2

and Sn2 = Sum of n terms

Given  =

Required to find

=

We have  =

or  =

or =

Taking  = 17 or n = 34 + 1 = 35, we have  =  =