Nth term of 70, 100, 130

Mathematics

1 answer:

BlackZzzverrR [31]3 years ago

6 0

Answer:

a1 = 70

a2 = 100

a3 = 130

an = 70 + 30(n - 1)

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tester [92]

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

$\bf \textit{inverse proportional variation}\\\\
\begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
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\\
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\end{array}$

$\bf \\\\
-------------------------------\\\\
\textit{z varies directly with x}\implies z=kx
\\\\
\textit{and inversely with y}\implies z=\cfrac{kx}{y}
\\\\\\
\textit{we also know that}\quad 
\begin{cases}
x=6\\
y=2\\
z=15
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$\bf \cfrac{30}{6}=k\implies \boxed{5=k}\impliedby \textit{constant of variation}
\\\\\\
thus\implies z=\cfrac{5x}{y}\\\\
-------------------------------\\\\
\textit{what's "z" when }
\begin{cases}
x=4\\
y=9
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