Answer :
You have to determine wich consecutive numbers can be added to give 15 as a result. (Whole numbers)
a.
Let x be the first number and x+1 be the consecutive number.
If you add them the result should be 15:
[tex]\begin{gathered} x+x+1=15 \\ 2x+1=15 \\ 2x=15-1 \\ 2x=14 \\ \frac{2x}{2}=\frac{14}{2} \\ x=7 \end{gathered}[/tex]The first number is 7 and the consecutive number is x+1=7+1=8
So the first consecutive numbers that add up to 15 are
[tex]7+8=15[/tex]b. Now you have to find 3 consecutive numbers that add up to 15.
Let "x" be the smaller number, the next number will be "x+1" and the third number will be "x+2"
Add them up:
[tex]\begin{gathered} x+(x+1)+(x+2)=15 \\ x+x+1+x+2=15 \\ 3x+3=15 \\ 3x=15-3 \\ 3x=12 \\ \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}[/tex]The first number is x=4, then the next number is x+1=4+1=5, and the third one will be x+2=4+2=6.
The three consecutive numbers that add up to 15 are:
[tex]4+5+6=15[/tex]c. Finally you have to find 5 consecutive numbers that add up to 15. Following the same method as before, the first number will be represented by "x", then the following numbers will be "x+1", "x+2", "x+3" and "x+4"
[tex]\begin{gathered} x+(x+1)+(x+2)+(x+3)+(x+4)=15 \\ 5x+10=15 \\ 5x=15-10 \\ 5x=5 \\ \frac{5x}{5}=\frac{5}{5} \\ x=1 \end{gathered}[/tex]The 5 consecutive numbers that add up to 15 are
[tex]1+2+3+4+5=15[/tex]