Answer:
[tex]30^{th}[/tex] term = 3.5 pounds
[tex]30^{th}[/tex] term represents the amount of dog food at the beginning of the [tex]30^{th}[/tex] day.
Step-by-step explanation:
1st term = [tex]18[/tex] ⇒[tex]18-0*0.5[/tex]
2nd term = [tex]18-0.5[/tex] ⇒[tex]18-1*0.5[/tex]
3rd term = [tex]18-0.5-0.5[/tex] ⇒[tex]18-2*0.5[/tex]
It will follow the same pattern until the value is 0.
So we can observe that in the [tex]1^{st}[/tex] term there are no "0.5" terms.
In the [tex]2^{nd}[/tex] term we have 1 "0.5" term and in the [tex]3^{rd}[/tex] term we have 2 "0.5" terms.
It is clear that the number of "0.5" terms are always 1 less than the term that we are in.
So we can write the term for the [tex]30^{th}[/tex] term as;
[tex]18-(30-1)*0.5[/tex]
[tex]18-29*0.5[/tex]
=3.5 pounds
[tex]1^{st}[/tex] term represents the amount of dog food at the beginning of the [tex]1^{st}[/tex] day.
[tex]2^{nd}[/tex] term represents the amount of dog food at the beginning of the [tex]2^{nd}[/tex] day.
Same with the [tex]3^{rd}[/tex] term.
So we can say that [tex]30^{th}[/tex] term represents the amount of dog food at the beginning of the [tex]30^{th}[/tex] day.
