Q. 33

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

Answer :

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

To find: the ratio of 18th 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 18th term is required of both AP’s which is



Substituting n = 35 in (i) we get



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