<PRE><B>Question 1209375</B>
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I agree with the other tutor. The way this problem is set up leads to a contradiction.
a&lt;sub&gt;1&lt;/sub&gt;+a&lt;sub&gt;3&lt;/sub&gt;+a&lt;sub&gt;5&lt;/sub&gt; = 5
a&lt;sub&gt;2&lt;/sub&gt;+a&lt;sub&gt;4&lt;/sub&gt; = -2


Add the equations to arrive at
a&lt;sub&gt;1&lt;/sub&gt;+a&lt;sub&gt;2&lt;/sub&gt;+a&lt;sub&gt;3&lt;/sub&gt;+a&lt;sub&gt;4&lt;/sub&gt;+a&lt;sub&gt;5&lt;/sub&gt; = 3
which means
S&lt;sub&gt;5&lt;/sub&gt; = 3


S&lt;sub&gt;5&lt;/sub&gt; represents the sum of the first 5 terms of the arithmetic sequence.


S&lt;sub&gt;n&lt;/sub&gt; = sum of the first n terms of an arithmetic sequence
S&lt;sub&gt;n&lt;/sub&gt; = (n/2)*(a&lt;sub&gt;1&lt;/sub&gt; + a&lt;sub&gt;n&lt;/sub&gt;)
S&lt;sub&gt;5&lt;/sub&gt; = (5/2)*(a&lt;sub&gt;1&lt;/sub&gt; + a&lt;sub&gt;5&lt;/sub&gt;)
3 = 2.5*(a&lt;sub&gt;1&lt;/sub&gt; + a&lt;sub&gt;5&lt;/sub&gt;)
a&lt;sub&gt;1&lt;/sub&gt; + a&lt;sub&gt;5&lt;/sub&gt; = 3/(2.5)
a&lt;sub&gt;1&lt;/sub&gt; + a&lt;sub&gt;5&lt;/sub&gt; = 1.2


a&lt;sub&gt;1&lt;/sub&gt;+a&lt;sub&gt;3&lt;/sub&gt;+a&lt;sub&gt;5&lt;/sub&gt; = 5
(a&lt;sub&gt;1&lt;/sub&gt;+a&lt;sub&gt;5&lt;/sub&gt;)+a&lt;sub&gt;3&lt;/sub&gt; = 5
1.2+a&lt;sub&gt;3&lt;/sub&gt; = 5
a&lt;sub&gt;3&lt;/sub&gt; = 5-1.2
&lt;font color=blue&gt;a&lt;sub&gt;3&lt;/sub&gt; = 3.8&lt;/font&gt;


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Then consider:
a&lt;sub&gt;2&lt;/sub&gt;+a&lt;sub&gt;4&lt;/sub&gt; = -2
(a&lt;sub&gt;3&lt;/sub&gt;-d)+(a&lt;sub&gt;3&lt;/sub&gt;+d) = -2
2*a&lt;sub&gt;3&lt;/sub&gt; = -2
a&lt;sub&gt;3&lt;/sub&gt; = -2/2
&lt;font color=red&gt;a&lt;sub&gt;3&lt;/sub&gt; = -1&lt;/font&gt;


But this contradicts &lt;font color=blue&gt;a&lt;sub&gt;3&lt;/sub&gt; = 3.8&lt;/font&gt; found in the previous section.
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