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Common terms of two arithmetic progressions

This type of question, asked 7 times: 29 Jun 2022, 30 Jan 2023, 1 Feb 2023, 27 Jan 2024, 1 Feb 2024, 4 Apr 2025, 2 Apr 2026 S1. All 7 questions below, oldest first.

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  1. Question 1

    29 Jun 2022

    173
    Let 3,6,9,12,…3,6,9,12,\ldots upto 78 terms and 5,9,13,17,…5,9,13,17,\ldots upto 59 terms be two series. Then, the sum of the terms common to both the series is equal to

  2. Question 2

    30 Jan 2023

    175
    The 8th 8^{\text{th~}} common term of the series
    S1=3+7+11+15+19+⋯ .S2=1+6+11+16+21+⋯ .\begin{matrix} & S_{1}= 3 + 7 + 11 + 15 + 19 + \cdots. \\ & S_{2}= 1 + 6 + 11 + 16 + 21 + \cdots. \end{matrix}
    Is

  3. Question 3

    1 Feb 2023

    179
    The sum of the common terms of the following three arithmetic progressions.
    3,7,11,15,……,3993,7,11,15,\ldots\ldots,399
    2,5,8,11,……,3592,5,8,11,\ldots\ldots,359 and
    2,7,12,17,……,1972,7,12,17,\ldots\ldots,197
    is equal to

  4. Question 4

    27 Jan 2024

    66
    The number of common terms in the progressions 4,9,14,19,….4,9,14,19,\ldots.. , up to 25th 25^{\text{th~}} term and 3,6,9,123,6,9,12, ......., up to 37th 37^{\text{th~}} term is :

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  5. Question 5

    1 Feb 2024

    84
    Let 3,7,11,15,….,4033,7,11,15,\ldots.,403 and 2,5,8,11,…,4042,5,8,11,\ldots,404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to

  6. Question 6

    4 Apr 2025

    53
    Let A={1,6,11,16,…}A\mathbf{= \{ 1,6,11,16,\ldots\}} and B={9,16,23,30,…}B\mathbf{= \{ 9,16,23,30,\ldots\}} be the sets consisting of the first 2025 terms of two arithmetic progressions. Then n(A∪B)n(A\cup B) is.

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  7. Question 7

    2 Apr 2026 S1

    55
    Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 6. Then the number of elements in A∩BA\cap B, which are divisible by 3 , is :

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