Question 1203500
<pre>

General terms for sequences are not unique.  How about this general term:

{{{a[n]}}}{{{""=""}}}{{{expr(-1/8)(27n^4-306n^3+1197n^2-1878n+968)}}}

It's more complicated, but it works:

{{{a[1]}}}{{{""=""}}}{{{expr(-1/8)(27*1^4-306*1^3+1197*1^2-1878*1+968)}}}{{{""=""}}}{{{expr(-1/8)(27*1-306*1+1197*1-1878*1+968){{{""=""}}}{{{expr(-1/8)(27-306+1197-1878+968)}}}{{{""=""}}}{{{expr(-1/8)(8)}}}{{{""=""}}}{{{-1}}}

{{{a[2]}}}{{{""=""}}}{{{expr(-1/8)(27*2^4-306*2^3+1197*2^2-1878*2+968)}}}{{{""=""}}}{{{expr(-1/8)(27*16-306*8+1197*4-1878*2+968){{{""=""}}}{{{expr(-1/8)(432-2448+4788-3756+968)}}}{{{""=""}}}{{{expr(-1/8)(-16)}}}{{{""=""}}}{{{2}}}

{{{a[3]}}}{{{""=""}}}{{{expr(-1/8)(27*3^4-306*3^3+1197*3^2-1878*3+968)}}}{{{""=""}}}{{{expr(-1/8)(27*81-306*27+1197*9-1878*3+968){{{""=""}}}{{{expr(-1/8)(2187-8262+10773-5634+968)}}}{{{""=""}}}{{{expr(-1/8)(32)}}}{{{""=""}}}{{{-4}}}

{{{a[4]}}}{{{""=""}}}{{{expr(-1/8)(27*4^4-306*4^3+1197*4^2-1878*4+968)}}}{{{""=""}}}{{{expr(-1/8)(27*256-306*64+1197*16-1878*4+968){{{""=""}}}{{{expr(-1/8)(6912-19584+19152-7512+968)}}}{{{""=""}}}{{{expr(-1/8)(-64)}}}{{{""=""}}}{{{8}}}

{{{a[5]}}}{{{""=""}}}{{{expr(-1/8)(27*5^4-306*5^3+1197*5^2-1878*5+968)}}}{{{""=""}}}{{{expr(-1/8)(27*625-306*125+1197*25-1878*5+968){{{""=""}}}{{{expr(-1/8)(16875-38250+29925-9390+968)}}}{{{""=""}}}{{{expr(-1/8)(128)}}}{{{""=""}}}{{{-16}}}

I gave this only as an enrichment example for you.  This is not the general term
your teacher expected you to give.  The other tutors gave you that one.  This is
just to show you that there are more than one general term for any given finite
number of terms of a sequence.

If you calculate the 6th term using this general term, you will find it to be
-211, not 32, which is what you will get as the 6th term using the general term
for a geometric sequence.

Edwin</pre>