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Terms of an A.P. with given sum and product

This type of question, asked 2 times: 4 Apr 2025, 24 Jan 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    4 Apr 2025

    140
    Consider two sets AA and BB, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the elements of BB be 36 and q respectively. Let d and D be the common differences of AP's in A and B respectively such that D=d+3, d>0D = d + 3,\text{ }d > 0. If p+qp−q=195\frac{p + q}{p - q}=\frac{19}{5}, then p−qp - q is equal to.

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  2. Question 2

    24 Jan 2026 S2

    55
    Let α1,α2,α3,α4\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{4} be an A.P. of four terms such that each term of the A.P. and its common difference ll are integers. If α1+α2+α3+α4=48\alpha_{1}+\alpha_{2}+\alpha_{3}+\alpha_{4}= 48 and α1α2α3α4+l4=361\alpha_{1}\alpha_{2}\alpha_{3}\alpha_{4}+l^{4}= 361, then the largest term of the A.P. is equal to

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