Question

You have 7 consecutive numbers, with the smallest number n.
a) What are the 7 numbers in terms of n?
b) Hence what is the sum of all the numbers?

Answer 1

(a) The seven consecutive numbers are $n,n+1,n+2,n+3,n+4,n+5,n+6$.

(b) The sum of all the seven consecutive numbers is $7n+21$.

Given:

The smallest number in the seven consecutive numbers is $n$.

Explanation:

(a)

The gap between two consecutive numbers is always $1$. It means we can add $1$ in the current number to get the next number.

First number is $n$, so the second number is $n+1$ and the third number is $(n+1)+1$ that is $n+2$.

Fourth number: $(n+2)+1=n+3$

Fifth number: $(n+3)+1=n+4$

Sixth number: $(n+4)+1=n+5$

Seventh number: $(n+5)+1=n+6$

Therefore, seven consecutive numbers are $n,n+1,n+2,n+3,n+4,n+5,n+6$.

(b)

The sum of these seven consecutive numbers is:

$\text{Sum}=n+(n+1)+(n+2)+(n+3)+(n+4)+(n+5)+(n+6)$

$\text{Sum}=(n+n+n+n+n+n+n)+(1+2+3+4+5+6)$

$\text{Sum}=7n+21$

Therefore, the sum of all the seven consecutive numbers is $7n+21$.

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