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A.P. with one fixed term: make a product of terms least or greatest

This type of question, asked 2 times: 31 Jan 2023, 29 Jan 2024. All 2 questions below, oldest first.

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  1. Question 1

    31 Jan 2023

    162
    Let a1,a2,a3,…a_{1},a_{2},a_{3},\ldots be an A.P. If a7=3a_{7}= 3, the product a1a4a_{1}a_{4} is minimum and the sum of its first nn terms is zero, then n!−4an(n+2)n! - 4a_{n(n + 2)} is equal to:

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  2. Question 2

    29 Jan 2024

    62
    In an A.P., the sixth terms a6=2a_{6}= 2. If the a1a4a5a_{1}a_{4}a_{5} is the greatest, then the common difference of the A.P., is equal to

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