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a22 = -49 and a25 = -58

Find a1

Guest Jun 17, 2015

Best Answer 

 #2
avatar+18715 
+10

$$\small{\text{$
\mathbf{
a_{22} = -49 \quad \mathrm{and} \quad a_{25}= -58 \quad \mathrm{find} \quad a_1
}
$}}$$

 

$$\mathbf{
\mathrm{Explicit~ Formula:}
& \quad a_n = a_1 + (n-1)\cdot d
} \\\\
\small{\text{$
\begin{array}{lrcl}
& a_{22} &=& a_1 + 21 \cdot d \\
& a_{25} &=& a_1 + 24 \cdot d \\
\\
\hline
\\
& a_{22} - a_1 &=& 21 \cdot d \\
& a_{25} - a_1 &=& 24 \cdot d \\
\\
\hline
\\
& \dfrac{ a_{22} - a_1 } { a_{25} - a_1 } &=& \dfrac{21} {24}\\ \\
& \dfrac{ a_{22} - a_1 } { a_{25} - a_1 } &=& \dfrac{7} {8}\\\\
& 8\cdot ( a_{22} - a_1 ) &=& 7\cdot ( a_{25} - a_1 )\\
& 8\cdot a_{22} - 8\cdot a_1 &=& 7\cdot a_{25} - 7\cdot a_1\\
& 8\cdot a_1 - 7\cdot a_1 &=& 8\cdot a_{22} - 7\cdot a_{25} \\
& \mathbf{a_1} &\mathbf{=}& \mathbf{8\cdot a_{22} - 7\cdot a_{25}} \\\\
& a_1 &=& 8\cdot (-49) - 7 \cdot (-58 ) \\
& a_1 &=& -392 + 406 \\
& \mathbf{a_1} &\mathbf{=}& \mathbf{14}
\end{array}
$}}$$

 

heureka  Jun 18, 2015
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2+0 Answers

 #1
avatar+78744 
+5

-58 - (-49)  = -9     is the difference in these terms which seems to imply that  -9/3 = -3 is the common difference between terms

 

So......

 

-58  = a1 + d(n - 1)              

 

-58   = a1 - 3(25 - 1)

 

-58  = a1 - 72    add 72 to both sides

 

14  = a1

 

 

CPhill  Jun 18, 2015
 #2
avatar+18715 
+10
Best Answer

$$\small{\text{$
\mathbf{
a_{22} = -49 \quad \mathrm{and} \quad a_{25}= -58 \quad \mathrm{find} \quad a_1
}
$}}$$

 

$$\mathbf{
\mathrm{Explicit~ Formula:}
& \quad a_n = a_1 + (n-1)\cdot d
} \\\\
\small{\text{$
\begin{array}{lrcl}
& a_{22} &=& a_1 + 21 \cdot d \\
& a_{25} &=& a_1 + 24 \cdot d \\
\\
\hline
\\
& a_{22} - a_1 &=& 21 \cdot d \\
& a_{25} - a_1 &=& 24 \cdot d \\
\\
\hline
\\
& \dfrac{ a_{22} - a_1 } { a_{25} - a_1 } &=& \dfrac{21} {24}\\ \\
& \dfrac{ a_{22} - a_1 } { a_{25} - a_1 } &=& \dfrac{7} {8}\\\\
& 8\cdot ( a_{22} - a_1 ) &=& 7\cdot ( a_{25} - a_1 )\\
& 8\cdot a_{22} - 8\cdot a_1 &=& 7\cdot a_{25} - 7\cdot a_1\\
& 8\cdot a_1 - 7\cdot a_1 &=& 8\cdot a_{22} - 7\cdot a_{25} \\
& \mathbf{a_1} &\mathbf{=}& \mathbf{8\cdot a_{22} - 7\cdot a_{25}} \\\\
& a_1 &=& 8\cdot (-49) - 7 \cdot (-58 ) \\
& a_1 &=& -392 + 406 \\
& \mathbf{a_1} &\mathbf{=}& \mathbf{14}
\end{array}
$}}$$

 

heureka  Jun 18, 2015

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