Answer:
10 friends
Step-by-step explanation:
we know that
The formula of the sum is equal to
[tex]sum=\frac{n}{2}[2a1+(n-1)d][/tex]
where
a1 is the first term
n is the number of terms (number of friends)
d is the common difference in the arithmetic sequence
In this problem we have
[tex]sum=275\ stickers[/tex]
[tex]a1=5\ stickers[/tex]
[tex]d=5[/tex] ----> the common difference
substitute in the formula and solve for n
[tex]275=\frac{n}{2}[2(5)+(n-1)(5)][/tex]
[tex]550=n[10+5n-5]\\ \\550=10n+5n^{2} -5n\\ \\5n^{2}+5n-550=0[/tex]
Solve the quadratic equation by graphing
The solution is n=10
see the attached figure
therefore
She had 10 friends who got stickers
