Question

Hello! I got -560 just want to confirm my answer. Thanks!

Answer 1

Explanation

We are given the following series:

`12+4-4-12-20-...`

We are required to determine the sum of the first 14 terms of the given series.

This is achieved thus:

We know that the sum of n terms of a series is given as:

`\begin{gathered} S_n=(n)/(2)[2a+(n-1)d] \\ where \\ a=first\text{ term} \\ d=common\text{ difference} \\ n=number\text{ of terms} \end{gathered}`

Therefore, we have:

`\begin{gathered} S_n=(n)/(2)[2a+(n-1)d] \\ where \\ a=12 \\ d=4-12=-8 \\ n=14 \\ \\ \therefore S_(14)=(14)/(2)[2\cdot12+(14-1)-8] \\ S_(14)=7[24+(13)-8] \\ S_(14)=7(24-104) \\ S_(14)=7\cdot-80 \\ S_(14)=-560 \end{gathered}`

Hence, the answer is:

`S_(14)=-560`