Question 980362
{{{a[n]=a[1]+(n-1)*d}}}
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{{{a[5]=a[1]+(5-1)*d}}}
1.{{{a[1]+4d=9}}}
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{{{a[32]=a[1]+(32-1)*d}}}
2.{{{a[1]+31d=-84}}}
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Subtract eq. 1 from eq. 2,
{{{a[1]+31d-a[1]-4d=-84-9}}}
{{{27d=-93}}}
{{{d=-93/27}}}
{{{d=-31/9}}}
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So then,
{{{a[1]+4(-31/9)=9}}}
{{{a[1]-124/9=81/9}}}
{{{a[1]=205/9}}}
and
{{{a[23]=205/9+(23-1)(-31/9)}}}
{{{a[23]=205/9-682/9}}}
{{{a[23]=-477/9}}}
{{{highlight_green(a[23]=-53)}}}