# arrow_back Determine the values of $x$ and $y$ in the sequence $7 ; x ; y ;-11 ; \ldots$

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Determine the values of $x$ and $y$ in the sequence $7 ; x ; y ;-11 ; \ldots$

$x=1$ and $y=-5$

Explanation:

\begin{aligned}
7 ; x ; y ; &-11 ; \ldots \\
a &=7 \\
a+3 d &=-11 \\
7+3 d &=-11 \\
d &=-6 \\
x &=a+d=7+(-6)=1 \\
y &=a+2 d=7+2(-6)=-5
\end{aligned}

OR

\begin{aligned}
a+3 d &=-11 \\
3 d &=-11-7 \\
3 d &=-18 \\
d &=-6 \\
x &=1 \\
y &=-5
\end{aligned}

OR

\begin{aligned}
&x-7=y-x \quad \text { and } \quad y-x=-11-y \\
&2 x-7=y \quad 2 y=-11+x \ldots(1) \quad \\
&(1) \text { into }(2) \\
&2(2 x-7)=-11+x \\
&4 x-14=-11+x \\
&3 x=3 \\
&x=1 \\
&y=2(1)-7=-5
\end{aligned}

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