<PRE><B>Question 1209569</B>
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Answer: &lt;font color=red&gt;x = 40&lt;/font&gt;


Explanation


1, 4, 7, 10, ... is an arithmetic sequence
a&lt;sub&gt;1&lt;/sub&gt; = 1 is the first term
d = 3 is the common difference.


S&lt;sub&gt;n&lt;/sub&gt; = sum of the first n terms
S&lt;sub&gt;n&lt;/sub&gt; = 0.5n*(2*a&lt;sub&gt;1&lt;/sub&gt;+d*(n-1))
287 = 0.5n*(2*1+3*(n-1))
1.5n^2-0.5n-287 = 0


Using the quadratic formula will yield solutions n = -13.667 (approximate) and n = 14.
We ignore the negative value of n. 
n must be a positive whole number 1,2,3,etc
I&#39;ll let the student handle the scratch work for the quadratic formula.


We determined there are 14 terms being added in {1,4,7,10,...,x} to yield the sum 287.


Let&#39;s determine the 14&lt;sup&gt;th&lt;/sup&gt; term.
a&lt;sub&gt;n&lt;/sub&gt; = a&lt;sub&gt;1&lt;/sub&gt; + d(n-1)
a&lt;sub&gt;n&lt;/sub&gt; = 1 + 3*(n-1)
a&lt;sub&gt;n&lt;/sub&gt; = 3n-2
a&lt;sub&gt;14&lt;/sub&gt; = 3*14-2
a&lt;sub&gt;14&lt;/sub&gt; = &lt;font color=red&gt;40&lt;/font&gt;


Therefore, &lt;font color=red&gt;x = 40&lt;/font&gt; and 1+4+7+10+...+&lt;font color=red&gt;40&lt;/font&gt; = 287


Verification using &lt;a href=&quot;https://www.wolframalpha.com/input?i=1%2B4%2B7%2B10%2B...%2B40+%3D+287&quot;&gt;WolframAlpha&lt;/a&gt;
Another way to confirm is to use a spreadsheet. 
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