The sums of n terms of two arithmetic progressions are in the ratio `5n + 4 : 9n + 6`. Find the ratio of their `18^(t h)`terms.

Explanation

To solve the problem, we need to find the ratio of the 18th terms of two arithmetic progressions (APs) given that the sums of their first n terms are in the ratio \(5n + 4 : 9n + 6\).

### Step 1: Understand the formula for the sum of n terms of an AP
The sum of the first n terms \(S_n\) of an arithmetic progression can be expressed as:
\[ S_n = \frac{n}{2} \left(2a + (n-1)d\right) \]
where \(a\) is the first term and \(d\) is the common difference.
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