Question
Find the sum of all natural numbers from 1 to 300 which
are divisible by 7.Solution
Numbers divisible by 7 between 1 and 300 are: 7, 14, 21, …, 294 This is an arithmetic progression (AP): First term a = 7 Common difference d = 7 Last term l = 294 Find number of terms n: l = a + (n − 1)d 294 = 7 + (n − 1)×7 294 − 7 = 7(n − 1) 287 = 7(n − 1) n − 1 = 41 n = 42 Sum of n terms of AP: S = n/2 × (first + last) = 42/2 × (7 + 294) = 21 × 301 = 21 × 300 + 21 × 1 = 6,300 + 21 = 6,321
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