Question 1107560
<pre>
If you are studying arithmetic sequences (progressions), this is the way
you should do it.

Bridget's is an arithmetic sequence (progression) with a<sub>1</sub>=6+3=9 and d=3.
So her number of books on the nth week is 

{{{a[n]=a[1]+(n-1)d}}}
{{{a[n]=9+(n-1)*3}}}

Cole's is an arithmetic sequence with a<sub>1</sub>=38+1=39 and d=1.
So his number of books on the nth week is

{{{a[n]=a[1]+(n-1)d}}}
{{{a[n]=39+(n-1)1}}}

Set them equal:

{{{9+(n-1)3}}}{{{""=""}}}{{{39+(n-1)1}}}

Simplify and solve for n.  You'll get 16 weeks.

Edwin</pre>