She gives away n books per week, so If [tex] w [/tex] [tex] =week number [/tex] , then she has ([tex] 100-nw [/tex]) books left at any time.
this will be the explicit formula.
so we need to write in terms of recrusive.
to be recrusive each term must be expressed in terms of previous term.
in this represent [tex] a_{w[tex] +1 [/tex]} [/tex] in terms of [tex] a_{w} [/tex]
[tex] a_{w} =100-n(w-1) [/tex]
[tex] a_{w+1} =100-n(w+1-1) [/tex]
replace w+1 in place of w .
[tex] a_{W+1} =100-nw [/tex][tex] a_{w} =a_{w+1} +n [/tex].
[tex] a_{w} -n=a_{w+1} [/tex]. this will be the recrusive expression for number of books she left.
