Question

What is the sum of the first five terms in this series?3+(-9)+27+(-81)+…A. 243B. -9C. 183D. 61

Answer 1

Notice that:

$\begin{gathered} 3=(-1)^{1+1}*3^1, \\ -9=(-1)^{2+1}*3^2, \\ 27=(-1)^{3+1}*3^3, \\ -81=(-1)^{4+1}*3^4. \end{gathered}$

Therefore the fifth term of the sequence in the series is:

$(-1)^{5+1}*3^5=243.$

Then the sum of the first 5 terms in the given series is:

$3+(-9)+27+(-81)+243=3-9+27-81+243.$

Simplifying the above result we get:

$3-9+27-81+243=183.$

Answer: Option C.