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    Question

    Find the sum of all multiples of 9 between 1 and 100

    (including both ends if applicable).
    A 594 Correct Answer Incorrect Answer
    B 625 Correct Answer Incorrect Answer
    C 770 Correct Answer Incorrect Answer
    D 529 Correct Answer Incorrect Answer

    Solution

    First multiple of 9 in this range: 9 Last multiple less than or equal to 100: 99 Sequence: 9, 18, 27, …, 99 (AP with a = 9, d = 9) Number of terms n: 99 = 9 + (n βˆ’ 1) Γ— 9 99 βˆ’ 9 = 9(n βˆ’ 1) 90 = 9(n βˆ’ 1) β‡’ n βˆ’ 1 = 10 β‡’ n = 11 Sum = n/2 Γ— (first + last) = 11/2 Γ— (9 + 99) = 11/2 Γ— 108 = 11 Γ— 54 = 594 Answer: 594.

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