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What is the sum of the geometric sequence 1, -6, 36, ... if there are 6 terms?

Answer 1

If the first term of a geometric sequence is \(\Large a\) and the common ratio is \(\Large r\), then:
-the second term is \(\Large ar\);
-the third term is \(\Large ar^2\);
etc. In general, the nth term is \(\Large ar^{n−1}\)
If we sum the first \(\Large n\) terms of a geometric series, we obtain:
\(\Large S_n=a+ar+....+ar^{n−2}+ar^{n−1}\)

So,the geometric sequence 1, -6, 36,... has \(\Large a=1, r=-6,n=6\)
the sum:\(\Large S=1-6+36-216+1296-7776=-6665\)