Question
Find the sum of all natural numbers less than 500 which are divisible by 7.
Solution
Smallest multiple of 7: 7 Largest multiple of 7 less than 500: 7 × 71 = 497 So series: 7, 14, ..., 497 is an AP with a = 7, d = 7, last term l = 497 Number of terms n: l = a + (n−1)d ⇒ 497 = 7 + (n−1)7 497 − 7 = 7(n − 1) ⇒ 490 = 7(n − 1) n − 1 = 70 ⇒ n = 71 Sum = n/2 × (first + last) = 71/2 × (7 + 497) = 71/2 × 504 = 71 × 252 = 17,892.
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