Question 1205120
<br>
The statement of the problem has (at least) three faults.<br>
(1) "n" and "N" are used interchangeably to represent the same thing.
(2) The form "Pn=Pn+ Blank" is not appropriate for a recursive formula.  In fact, if that form is correct, then "Blank" is 0.
(3) The form "Pn= N+" is not appropriate for an explicit formula.<br>
Since the number sold in week 1 is P(0), the number sold in week (n+1) is P(n).<br>
Part 1 -- recursive formula<br>
The recursive formula for the number sold in week (n+1) tells the number sold as a function of the number sold in week n.  The number sold in week n is P(n-1); and since the number sold increases by the same number 8 in each week, the recursive formula for the number sold in week (n+1) is<br>
P(n)=P(n-1)+8<br>
Part 2 -- explicit formula<br>
The explicit formula for the number sold in week (n+1) is a linear equation in the form<br>
y=mx+b<br>
or, in this problem,<br>
P(n)=mn+b<br>
Since the number sold increases by 8 each week, m=8; and since P(0)=7, b=7 and the formula is<br>
P(n)=8n+7<br>
Part 3 -- number sold in week 6<br>
The number sold in week 6 is<br>
P(5) = 8(5)+7 = 47<br>