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 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

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