Mathematics: The first term of a arithmetic sequence is 2 and the 4th term is 11, how do i find the sum of the first 50 terms

The first term of a arithmetic sequence is 2 and

Ответ:

Shihhschool20

11.03.2022

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=2\\
a_4=11\\
n=4
\end{cases}
\\\\\\
a_4=2+(4-1)d\implies 11=2+(4-1)d\implies 11=2+3d
\\\\\\
9=3d\implies \cfrac{9}{3}=d\implies \boxed{3=d}\\\\
-------------------------------\\\\$

$\bf \textit{now, what's the 50th term anyway?}
\\\\\\
n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=2\\
n=50\\
d=3
\end{cases}
\\\\\\
a_{50}=2+(50-1)3\implies a_{50}=2+147\implies a_{50}=149\\\\
-------------------------------\\\\$

$\bf \textit{sum of a finite arithmetic sequence}\\\\
S_n=\cfrac{n}{2}(a_1+a_n)\quad 
\begin{cases}
n=50\\
a_1=2\\
a_{50}=149
\end{cases}\implies S_{50}=\cfrac{50}{2}(2+149)$

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Ответ:

Jasoncookies23

21.03.2020

Mathematics

I believe it would be 9a + 3b + c = 3 but it's been awhile since I've done this...

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The first term of a arithmetic sequence is 2 and the 4th term is 11, how do i find the sum of the first 50 terms

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