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Find the sum of the first 30 terms of the following arithmetic sequence:

  -10, -18, -26, -34, ...

 Dec 14, 2018

Best Answer 

 #1
avatar+22181 
+10

Find the sum of the first 30 terms of the following arithmetic sequence:

  -10, -18, -26, -34, ...

 

\(\begin{array}{|rcll|} \hline a_n &=& a_1+(n-1)d \\ a_n &=& -10 +(n-1)(-8) \\ a_n &=& -10-8n+8 \\ \mathbf{a_n} & \mathbf{=} & \mathbf{-2-8n } \\ a_{30} &=& -2-8\cdot 30 \\ \mathbf{a_{30}} & \mathbf{=} & \mathbf{-242} \\\\ s_n &=& \dfrac{a_1+a_n}{2}\cdot n \\ s_{30} &=& \dfrac{a_1+a_{30}}{2}\cdot 30 \\ s_{30} &=& \dfrac{-10-242}{2}\cdot 30 \\ s_{30} &=& -252 \cdot 15 \\ \mathbf{s_{30}} & \mathbf{=} & \mathbf{-3780} \\ \hline \end{array}\)

 

The sum of the first 30 terms is \(\mathbf{-3780}\)

 

laugh

 Dec 14, 2018
 #1
avatar+22181 
+10
Best Answer

Find the sum of the first 30 terms of the following arithmetic sequence:

  -10, -18, -26, -34, ...

 

\(\begin{array}{|rcll|} \hline a_n &=& a_1+(n-1)d \\ a_n &=& -10 +(n-1)(-8) \\ a_n &=& -10-8n+8 \\ \mathbf{a_n} & \mathbf{=} & \mathbf{-2-8n } \\ a_{30} &=& -2-8\cdot 30 \\ \mathbf{a_{30}} & \mathbf{=} & \mathbf{-242} \\\\ s_n &=& \dfrac{a_1+a_n}{2}\cdot n \\ s_{30} &=& \dfrac{a_1+a_{30}}{2}\cdot 30 \\ s_{30} &=& \dfrac{-10-242}{2}\cdot 30 \\ s_{30} &=& -252 \cdot 15 \\ \mathbf{s_{30}} & \mathbf{=} & \mathbf{-3780} \\ \hline \end{array}\)

 

The sum of the first 30 terms is \(\mathbf{-3780}\)

 

laugh

heureka Dec 14, 2018

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