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A.P. with given sums of odd-placed and even-placed terms

This type of question, asked 3 times: 14 Jun 2022, 22 Jan 2025, 2 Apr 2025. All 3 questions below, oldest first.

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  1. Question 1

    14 Jun 2022

    73
    If {ai}i=1n\left\{ a_{i} \right\}_{i = 1}^{n} where nn is an even integer, is an arithmetic progression with common difference 1 , and ∑i=1nai=192,∑i=1n/2a2i=120\sum_{i = 1}^{n} a_{i}= 192,\sum_{i = 1}^{n/2} a_{2i}= 120, then nn is equal to:

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  2. Question 2

    22 Jan 2025

    130
    Suppose that the number of terms in an A.P. is 2 k , k∈Nk \in N. If the sum of all odd terms of the A.P. is 40 , the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27 , then k is equal to

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  3. Question 3

    2 Apr 2025

    128
    The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by 212\frac{21}{2}. Then the number of terms which are integers in the A.P. is :

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