Answer:
On the 20th day he will have 125 baseball cards.
Step-by-step explanation:
We are given a statement that:
Everyday luis buys 5 more baseball cards to add to his collection . if he has 25 baseball cards before making any purchases.
We are asked to find how many will he have on day 20?
Let [tex]P_n[/tex] denotes the number of baseballs cards on nth day.
on the first day he will have:
[tex]P_1=25+5[/tex]
on second day he has:
[tex]P_2=P_1+5=25+5\times 2[/tex]
On third day he will have:
[tex]P_3=P_2+5=25+5\times 3[/tex]
and so on on the nth day he will have:
[tex]P_n=25+5\times n[/tex]
We are asked to find the number of baseball cards on 20th day.
i.e. n=20
[tex]P_{20}=25+5\times 20\\\\P_{20}=25+100\\\\P_{20}=125[/tex]
Hence, on the 20th day he will have 125 baseball cards.
