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The sum of n terms of two arithmetic pro...

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

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To solve the problem, we need to find the ratio of the 18th terms of two arithmetic progressions (APs) given that the sum of their n terms is in the ratio \(5n + 4 : 9n + 6\). ### Step-by-Step Solution: 1. **Understanding the Sum of n Terms of an AP**: The sum of the first \(n\) terms of an arithmetic progression can be expressed as: \[ S_n = \frac{n}{2} \times (2a + (n - 1)d) ...
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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.

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