Question
Average of thirteen consecutive numbers is 56. Find the
sum of smallest and largest number.Solution
Let the numbers be (a - 6), (a - 5), (a - 4), (a - 3), (a - 2), (a - 1), a, (a + 1), (a + 2), (a + 3), (a + 4), (a + 5) and (a + 6).
So, (a - 6 + a - 5 + a - 4 + a - 3 + a - 2 + a - 1 + a + a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + 6) ÷ 13 = 56
Or, (13a/13) = 56
Or, 'a' = 56
Required sum = a - 6 + a + 6 = 2a = 2 × 56 = 112
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