The sum of n terms of two ap are in ratio (5n+4) : (9n+6) Find the ratio of their 18th term?

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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.