Sequence problem

Apr 2010
43
1
\(\displaystyle
\sum_{k=1}^6(-1)^k4^k
\)

The answer is: 3276

How do you do this problem?
\(\displaystyle -1^6=1\)

\(\displaystyle 4^6=4096\)

4096 != 3276
Thanks.
 
Jun 2009
806
275
\(\displaystyle
\sum_{k=1}^6(-1)^k4^k
\)

The answer is: 3276

How do you do this problem?
\(\displaystyle -1^6=1\)

\(\displaystyle 4^6=4096\)

4096 != 3276
Thanks.
It is a GP with first term -4, common ratio r = -4 and number of terms 6.
So sum S = a[r^n - 1]/(r-1)
= -4(4096 - 1)/(-4-1)
Now find the answer.