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3 years ago

Find the common difference for the infinite arithmetic sequence shown.

Mathematics

1 answer:

mihalych1998 [28]3 years ago

4 0

The common difference is 12

Further explanation:

It is given that the infinite sequence is an arithmetic sequence

The common difference is the difference between consecutive terms of an arithmetic sequence.

Here,

$a_1 = 211\\a_2 = 223\\a_3 = 235\\a_4 = 247........$

The common difference is denoted by d.

Here,

$d = a_2-a_1 = 223-211 = 12\\a_3-a_2 = 235-223 = 12$

The common difference is same for all proceeding terms.

So,

d = 12

Keywords: Infinite arithmetic sequence, Common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

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$\bf \begin{array}{cccccclllll}
\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ k}}&\cdot&x
&& y={{ k }}x
\end{array}\\ \quad \\
$

and also

$\bf \begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x}
&&y=\cfrac{{{ k}}}{x}
\end{array}
$

now, we know that V varies directly to T and inversely to P simultaneously
thus $\bf V=T\cdot \cfrac{k}{P}$

so $\bf V=T\cdot \cfrac{k}{P}\qquad 
\begin{cases}
V=42\\
T=84\\
P=8
\end{cases}\implies 42=\cfrac{84k}{8}\implies 4=k
\\\\\\
V=\cfrac{4T}{P}\qquad now\quad 
\begin{cases}
V=74\\
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