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If the arithmetic progression whose comm...

If the arithmetic progression whose common difference is nonzero the sum of first `3n` terms is equal to the sum of next `n` terms. Then, find the ratio of the sum of the `2n` terms to the sum of next `2n` terms.

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To solve the problem, we need to find the ratio of the sum of the first `2n` terms of an arithmetic progression (AP) to the sum of the next `2n` terms, given that the sum of the first `3n` terms is equal to the sum of the next `n` terms. Let's denote: - The first term of the AP as \( a \) - The common difference as \( d \) ### Step 1: Write the formula for the sum of the first \( n \) terms of an AP The formula for the sum of the first \( n \) terms \( S_n \) of an AP is given by: ...
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