The average of 3 consecutive integers is 'k'. If the next two numbers are added, then the new average is:
let consecutive integers be x,x + 1,x + 2
average of 3 consecutive integers is 'k'Â
sum of 3 consecutive integers = 3k
$$ \frac{ x + x + 1 + x + 2 }{3} = k $$
$$ \frac{ 3x + 3 }{3} = k $$
x + 1 = k
x = k - 1
If the next two numbers are added,
$$ \frac{3k + x + 3 + x + 4}{5} $$
$$ \frac{3k + 2x + 7}{5} $$
$$ \frac{3k + 2(k - 1) + 7}{5} $$
$$ \frac{5k + 5}{5} = k + 1 $$
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