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vlabodo [156]
3 years ago
8

Find the sum of the first 17 terms of the arithmetic sequence 10, 14, 18, 22, 26...

Mathematics
2 answers:
kari74 [83]3 years ago
6 0
10, 14, 18 ....

notice, we get the next term by simply adding 4 to the current term, thus "4" is the "common difference, and we know that 10 is the first term.

\bf n^{th}\textit{ term of an arithmetic sequence}
\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=10\\
d=4\\
n=17
\end{cases}
\\\\\\
a_{17}=10+(17-1)(4)\implies a_{17}=10+(16)(4)
\\\\\\
a_{17}=10+64\implies a_{17}=74\\\\
-------------------------------

\bf \textit{ sum of a finite arithmetic sequence}
\\\\
S_n=\cfrac{n(a_1+a_n)}{2}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
----------\\
a_1=10\\
a_{17}=74\\
n=17
\end{cases}
\\\\\\
S_{17}=\cfrac{17(10+74)}{2}\implies S_{17}=\cfrac{17(84)}{2}\implies S_{17}=714
OLEGan [10]3 years ago
4 0
The answer would be 714.

Common difference =4An=A1+(n-1)dA17=10+(17-1)(4)=10+(16)(4)=10+64=74
Sn=n(a1+an)/2S17=17(10+74)/2=714<span />
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