Question 1158427
<pre>
4.5, −22.5, 112.5, −562.5, …

{{{matrix(5,5,

matrix(1,2,2nd,term)/matrix(1,2,1st,term),""="",(-22.5)/4.5,""="",-5,
"","","","","",
matrix(1,2,3rd,term)/matrix(1,2,2nd,term),""="",(112.5)/(-22.5),""="",-5,
"","","","","",
matrix(1,2,4th,term)/matrix(1,2,3rd,term),""="",(-562.5)/112.5,""="",-5)}}}

Since all those give the same answer, this is a geometric sequence with

first term = a<sub>1</sub> = 4.5 and common ratio r = -5.

To get a formula for any term, we use the general formula for the nth term
of a geometric sequence, use this

{{{matrix(1,3,
a[n],""="",a[1]r^(n-1))}}}

To get a formula for the sum of the first n terms, use this:

{{{matrix(1,3,
S[n],""="",a[1](r^n-1)/(r^""-1))}}}


Edwin</pre>