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.