Question

Can someone help me solve this please

Answer 1

n = 12

Explanation:

After you divide by 9, you have ...

`\displaystyle\sum\limits^n_(m=1)m=78`

The sum of numbers 1..n is given by ...

`\displaystyle\sum\limits^n_(m=1)m=(n(n+1))/(2)=78`

This resolves to the quadratic ...

n² +n -156 = 0

(n +1/2)² -156.25 = 0 . . . . . complete the square

n = -0.5 + √156.25 = -0.5 + 12.5

n = 12

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Comment on the sum

The sum of numbers 1 to n can be treated as the sum of the arithmetic series whose first term is 1 and whose last term is n. The average term is (1+n)/2, and the sum is the product of that and the number of terms:

n(n+1)/2 = sum of numbers 1 to n.