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Find the sum of the first 200 terms of 3 + 8 + 13 + 18 + ...

 Jun 2, 2020
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Find the sum of the first 200 terms of \(3 + 8 + 13 + 18 + \ldots\)

 

\(\begin{array}{|rcll|} \hline \mathbf{a_{200}=\ ? } \\ \hline a_n &=& a_1 + (n-1)*d \quad | \quad a_1 = 3 ,\ d=5 \\ a_n &=& 3 + (n-1)*5 \\ a_n &=& 3 + 5n-5 \\ a_n &=& 5n-2 \quad | \quad n = 200 \\ a_{200} &=& 5*200-2 \\ \mathbf{a_{200}} &=& \mathbf{998} \\ \hline \end{array}\)

 

\(\begin{array}{|rcll|} \hline \mathbf{sum=3 + 8 + 13 + 18 + \ldots + 998 } \\ \hline \text{sum} &=& \dfrac{(a_1+a_{200})}{2}*200 \\\\ \text{sum} &=& \dfrac{(3+998)}{2}*200 \\\\ \mathbf{\text{sum}} &=& \mathbf{100100} \\ \hline \end{array} \)

 

laugh

 Jun 2, 2020

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