Please explain an elementary algebra question for me...?

Question

QUESTION: "Write a formula for finding the sum s of 5 consecutive numbers, the smallest of which is n"

ANSWER: "S = 5N + 10".

Can someone explain this please? I thought it was just S = 5N. Where does the + 10 come from? Many thanks.

Answer 1

Consecutive numbers differ by 1.
If the first one is n, then the second one is n+1
That means the third one is the second number plus one (n+1)+1 = n+2
The fourth one is (n+2)+1 = n+3
and the fifth one is (n+3)+1 = n+4
Add them altogether
n + n+1 + n+2 + n+3 + n+4 = 5n + 10

Answer 2

Sometimes examples are the best ways to demonstrate the things we don't understand: If I chose the number 10,11,12,13,14,
then the formula would be S=5(10) + 10. The reason this works is because each of those numbers is the same thing as 10, but each consecutive number adds 1, then 2, then 3, then 4. (11-1=10) (12-2=10) (13-3=10)(etc.) 1+2+3+4=10, thats where the 10 comes from

Answer 3

s=5N + 10 is correct.

Let's consider 5 consecutive integers:

The smallest is n, the next is n+1, the next is n+2, and so on.

The sum will be

n+(n+1)+(n+2)+(n+3)+(n+4) =
5n+1+2+3+4=
5n+10!


There's your formula.

Answer 4

Smallest is n
Since consecutive, next is n+1

then, n+2,n+3,n+4
Sum S= n+(n+1)+(n+2)+(n+3)+(n+4)
= 5n+10!

Answer 5

its not 5n. 5n would be n times 5. you need consecutive numbers. so it would be n+(n+1)+(n+2)+(n+3)+(n+4).

Answer 6

it is a simplification

S = N + (N +1) + (N +2) + (N +3) + (N +4)
S = 5N + 10

Answer 7

N is smallest number
N + 1 is the next number
N + 2 is the number after that one
N + 3 is the next
N + 4 is the 5th number
Add them together
5N + 10