Question 1029340
<pre>
Checking to see if it is a geometric sequence:

{{{matrix(1,14,common,ratio,""="",

matrix(1,2,2nd,term)/matrix(1,2,1st,term),""="",3/4,"÷",3/5,""="",3/4,"×",5/3,""="",5/4)}}}

{{{matrix(1,14,common,ratio,""="",

matrix(1,2,3rd,term)/matrix(1,2,2nd,term),""="",15/16,"÷",3/4,""="",15/16,"×",4/3,""="",5/4)}}}

{{{matrix(1,14,common,ratio,""="",

matrix(1,2,4th,term)/matrix(1,2,3rd,term),""="",75/64,"÷",15/16,""="",75/64,"×",16/15,""="",5/4)}}}

So it is a geometric sequence with {{{a[1]=3/5}}} and {{{r=5/4}}}

The kth term is {{{a[k]=ar^(k-1)=expr(3/5)expr((5/4))^(k-1)}}}

In summation notation for the first n terms:

{{{sum(expr(3/5)expr((5/4))^(k-1),matrix(1,3,"","",k=1),matrix(1,5,"","","","",n))}}}

We may factor out the {{{3/5}}}

{{{expr(3/5)*sum(expr((5/4))^(k-1),matrix(1,3,"","",k=1),matrix(1,5,"","","","",n))}}}

Note: Your teacher may have wanted you to sum to infinity, instead
of only to n.  The reason I did not is because the series diverges 
since r > 1.

Edwin</pre>