Answer:
Recursive formula: [tex]c_n=c_{n-1}+3[/tex]
Explicit formula: [tex]c_n=3n[/tex]
Step-by-step explanation:
Let n be the number of week, [tex]c_n[/tex] be the number of albums Pam has on week n.
Every week she buys 3 new albums to keep her collection current, then
[tex]c_n=c_{n-1}+3[/tex]
{The number of albums Pam has on week n is the number of albums Pam has previous week increased by 3}
This is a recursive formula.
Suppose initially Pam has 0 albums. Then the first week she has 3 albums, the third week - 6 albums and so on. Mathematically
[tex]c_0=0\\ \\c_1=3=3\cdot 1\\ \\c_2=c_1+3=3+3=6=3\cdot 2\\ \\...[/tex]
The explicit formula is
[tex]c_n=3\cdot n[/tex]
