I completed a problem but it seems as if I got the wrong answer. I would like to see what error I made so I do not make the same mistake again. The questions goes as follows :
"If the sum of the first $n$ terms of a geometric series is given by $S_n = 1 - (-2)^n $, find the 4th term of the series."
I inputted 4 as n, as it stated it is the 4th term, and I got the following.
$S_4 = 1 - (-2)^4$
$S_4 = 1 + 16 $
$S_4 = 17 $
This answer was marked wrong, and the correct answer was -24. Can someone explain to me how the answer -24 can be obtained from this? Thanks.
$$S_n=u_1\frac {1-q^n}{1-q}$$
$$=3\frac {1-(-2)^n}{1-(-2)} $$
thus $$u_1=3$$ and $$q=-2$$
finally $$u_4=u_1q^3=-24$$