Question 1076234
<pre>
There are many possibilities

Could be this way:

5<sup>1</sup>-8 = 5-8 = -3
5<sup>2</sup>-8 = 25-8 = 17
5<sup>3</sup>-8 = 125-8 = 117
5<sup>4</sup>-8 = 625-8 = 617
...
{{{sum((5^k-8),k=1,n)}}}

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Or it could be this way:

-3+20 = 17
17+100 = 117
117+180 = 297
297+260 = 557
...
where we add terms of the arithmetic sequence 20,100,280,260,...
to each term to get the next term.

And the general term is a<sub>k</sub> = 40k<sup>2</sup>-100k+57
 
{{{sum((40k^2-100k+57),k=1,n)}}}

But there are trillions of other sequences that have -3,17,117
for their first three terms.  So how on earth could your teacher
expect you or anybody to guess which one he or she had in mind??

Edwin</pre>