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# help!

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The first term of an arithmetic sequence is −27 . The common difference of the sequence is 6.

What is the sum of the first 30 terms of the sequence?

Apr 27, 2020

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The first term of an arithmetic sequence is −27 . The common difference of the sequence is 6.

What is the sum of the first 30 terms of the sequence?

Formula: $$\begin{array}{|rcll|} \hline a_n &=& a_1 + (n-1)d \\ s_n &=& \left(\dfrac{a_1+a_n}{2} \right)\cdot n \\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline \mathbf{a_n} &=& \mathbf{a_1 + (n-1)d} \quad | \quad a_1=-27,\ n=30,\ d=6 \\\\ a_{30} &=& -27 + (30-1)\cdot 6 \\ a_{30} &=& -27 + 29\cdot 6 \\ a_{30} &=& -27 + 174 \\ \mathbf{a_{30}} &=& \mathbf{147} \\ \hline \mathbf{s_n} &=& \mathbf{\left(\dfrac{a_1+a_n}{2} \right)\cdot n} \quad | \quad n=30 \\\\ s_{30} &=& \left(\dfrac{a_1+a_{30}}{2} \right)\cdot 30 \quad | \quad a_1=-27,\ a_{30}=147 \\ s_{30} &=& \left(\dfrac{-27+147}{2} \right)\cdot 30 \\ s_{30} &=& \left(\dfrac{120}{2} \right)\cdot 30 \\ s_{30} &=& 60\cdot 30 \\ \mathbf{s_{30}} &=& \mathbf{1800} \\ \hline \end{array}$$ Apr 27, 2020