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A.P. of natural numbers fixed by a sum condition and an inequality

This type of question, asked 2 times: 27 Jul 2022, 29 Jan 2025. All 2 questions below, oldest first.

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  1. Question 1

    27 Jul 2022

    66
    Suppose a1,a2,…,an,…a_{1},a_{2},\ldots,a_{n},\ldots be an arithmetic progression of natural numbers. If the ratio of the sum of the first five terms to the sum of first nine terms of the progression is 5:175:17 and 110<a15<110 <a_{15}< 120 , then the sum of the first ten terms of the progression is equal to -

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  2. Question 2

    29 Jan 2025

    63
    Consider an A.P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800 . Then its 11th 11^{\text{th~}} term is :

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