Question

Write 84 as the sum of seven consecutive numbers

Answer 1

Step-by-step explanation:

Average = 84/7 =12

Average of the number is always the middle value. If there are seven numbers then average will be in the middle, three numbers will be greater than the average and the remaining three numbers will be smaller than the average. See the figure below:

So the biggest number is 15 and the smallest number is 9 and their difference is 15 - 9 = 6 .

Now let’s do it with algebraic method

Let smallest number is x

The 7 consecutive numbers are x, x+1, x+2, x+3, x+4, x+5 and x+6.

As per the question:

x + (x+1) + (x+2) + (x +3) + (x + 4) + (x+ 5) + (x + 6) = 84

7x + 1+2+3+4+5+6 = 84

7x +21 = 84

7x = 84 - 21

7x = 63

x = 9 (It is the smallest number)

x + 6 = 9 + 6 = 15 (It is the biggest number)

Difference = 15 - 9 = 6 → Answer.

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