Mathematics, 12.12.2019 02:31 offshoreext
Find the sum of the first 40 terms of the arithmetic sequence-3,1,
Answers: 2
or 
![\bf -3~~,~~\stackrel{-3+4}{1}~~,~~\stackrel{1+4}{5}~~,~~...\qquad \qquad \stackrel{\textit{common difference}}{d = 4} \\\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=-3\\ d= 4\\ n= 40 \end{cases} \\\\\\ a_{40}=-3+(40-1)4\implies a_{40}=-3+(39)4\implies a_{40}=153 \\\\[-0.35em] ~\dotfill](/tpl/images/0414/5899/5e026.png)
![\bf \textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\[-0.5em] \hrulefill\\ n = 40\\ a_{40}=153\\ a_1=-3 \end{cases}\implies S_{40}=\cfrac{40(-3+153)}{2} \\\\\\ S_{40}=20(150)\implies S_{40}=3000](/tpl/images/0414/5899/7424c.png)
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Find the sum of the first 40 terms of the arithmetic sequence-3,1,...
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