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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 step by step, we will use the properties of arithmetic progressions (AP) and the formula for the sum of the first n terms of an AP. ### Step-by-Step Solution: 1. **Understand the Problem**: We are given that the sum of the first n terms of two arithmetic progressions (AP1 and AP2) is in the ratio \(5n + 4 : 9n + 6\). We need to find the ratio of their 18th terms. 2. **Formula for Sum of n Terms**: The sum of the first n terms of an arithmetic progression is given by the formula: \[ ...
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