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

Let a ₁ , a ₂ , and d ₁ , d ₂ be the first terms and the common difference of the first and second arithmetic progression respectively.

According to the given condition,

Substituting n = 35 in (1), we obtain

From (2) and (3), we obtain

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

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