Question
Find the sum of all multiples of 9 between 1 and 100
(including both ends if applicable).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 − 1) × 9 99 − 9 = 9(n − 1) 90 = 9(n − 1) ⇒ n − 1 = 10 ⇒ n = 11 Sum = n/2 × (first + last) = 11/2 × (9 + 99) = 11/2 × 108 = 11 × 54 = 594 Answer: 594.
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