Question 121106

Notice that each term is increasing exponentially. So this sequence might be a geometric sequence. To find out, let's simply divide the terms.


First divide the 2nd term 15 by the 1st term 3 to get  

{{{15/3=5}}} 

 
Now divide the 3rd term 75 by the 2nd term 15 to get  

{{{75/15=5}}} 

 
Now divide the 4th term 375 by the 3rd term 75 to get  

{{{375/75=5}}} 

 

So if we pick any term and divide it by the previous term, we'll always get 5. This is the common ratio between the terms. So this means that {{{r=5}}}.


Now since we've started at 3, this means that {{{a=3}}}


Since the general geometric sequence is {{{a[n]=ar^n}}}, this means the sequence is


{{{a[n]=3*5^n}}}




Check:


Notice when n=0, then 


{{{a[0]=3*5^0=3*1=3}}}


and when n=1, then 


{{{a[1]=3*5^1=3*5=15}}}



and when n=2, then 


{{{a[2]=3*5^2=3*25=75}}}


and when n=3, then 


{{{a[3]=3*5^3=3*125=375}}}


and so on....