Question

Pam is a Disc Jockey. Every week she buys 3 new albums to keep her collection current. She currently owns 450 albums. a. Write a recursive formula for the number of albums Pam has b. Write an explicit formula for the number of albums Pam has

Answer 1

Answer:

Recursive formula: $c_n=c_{n-1}+3$

Explicit formula: $c_n=3n$

Step-by-step explanation:

Let n be the number of week, $c_n$ be the number of albums Pam has on week n.

Every week she buys 3 new albums to keep her collection current, then

$c_n=c_{n-1}+3$

{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

$c_0=0\\ \\c_1=3=3\cdot 1\\ \\c_2=c_1+3=3+3=6=3\cdot 2\\ \\...$

The explicit formula is

$c_n=3\cdot n$