The <em>first</em> eight terms of the sequence are 27, 27, 39, 87, 117.378, 147.755, 178.132 and 208.509.
<h3>
Determination of a given set of successive values of a sequence</h3>
By (1) we have that , and we simplify the system of equations as follows:
(2b)
(3b)
(4b)
By (2b), we simplify the system of equations once again:
(3c)
(4c)
And by equalising (3c) and (4c) we have an expression in terms of :
(5)
The roots of this <em>third order</em> polynomial are: , and . Since must be a <em>real</em> number, then .
By (4c) we have the value of :
By (2b) we find the value of :
And by (1) we find the value of :
The <em>first</em> eight terms are calculated below:
The <em>first</em> eight terms of the sequence are 27, 27, 39, 87, 117.378, 147.755, 178.132 and 208.509.
<h3>
Remark</h3>
<em>The statement present typing mistakes and is poorly formatted. Correct form is shown below:</em>
<em />
<em>The first four terms of an arithmetic sequence are: </em><em>, </em><em>, </em><em>, </em><em>. The first four terms of another sequence are: </em><em>, </em><em>, </em><em>, </em><em>. The eight terms satisfy:</em>
<em />
<em /><em> </em><em>(1)</em>
<em></em><em> </em><em>(2)</em>
<em></em><em> </em><em>(3)</em>
<em /><em> </em><em>(4)</em>
<em></em>
<em>By using the substitution </em><em>, or otherwise, find the all eight terms. </em>
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