Please solve: start with 2 and multiply by -3 repeatedly

Question

kasim17 · Answer

What the hell dude? When are you support to stop?

whpalmer4 · Answer

\[\begin{array}{cc}
 1 & 2 \
 2 & -6 \
 3 & 18 \
 4 & -54 \
 5 & 162 \
 6 & -486 \
 7 & 1458 \
 8 & -4374 \
 9 & 13122 \
 10 & -39366 \
 11 & 118098 \
 12 & -354294 \
 13 & 1062882 \
 14 & -3188646 \
 15 & 9565938 \
 16 & -28697814 \
 17 & 86093442 \
 18 & -258280326 \
 19 & 774840978 \
 20 & -2324522934 \
 21 & 6973568802 \
 22 & -20920706406 \
 23 & 62762119218 \
 24 & -188286357654 \
 25 & 564859072962 \
 26 & -1694577218886 \
 27 & 5083731656658 \
 28 & -15251194969974 \
 29 & 45753584909922 \
 30 & -137260754729766 \
 31 & 411782264189298 \
 32 & -1235346792567894 \
 33 & 3706040377703682 \
 34 & -11118121133111046 \
 35 & 33354363399333138 \
 36 & -100063090197999414 \
 37 & 300189270593998242 \
 38 & -900567811781994726 \
 39 & 2701703435345984178 \
 40 & -8105110306037952534 \
 41 & 24315330918113857602 \
 42 & -72945992754341572806 \
 43 & 218837978263024718418 \
 44 & -656513934789074155254 \
 45 & 1969541804367222465762 \
 46 & -5908625413101667397286 \
 47 & 17725876239305002191858 \
 48 & -53177628717915006575574 \
 49 & 159532886153745019726722 \
 50 & -478598658461235059180166 \
\end{array}\]Need more? :-)

kasim17 · Answer

Woah

tommynaut · Answer

If it's an equation you need, you could have it in the form
$$y = 2\times(-3)^{x}$$

whpalmer4 · Answer

Exercise for the reader: verify my answer (using pencil and paper) with @Tommynaut's formula for $x = 50$ :-)

whpalmer4 · Answer

Actually, we have a slight difference between our counting: I count "2" as the first number in the sequence, and he counts 2*(-3) = 6 as the first number in the sequence.  Compare my 50 with what you get with $x=49$ in his formula.

kasim17 · Answer

-300

tommynaut · Answer

If the question really just wants you to do that and keep going on forever, maybe the best way to write it out would be
$$\lim_{x \rightarrow \infty} y = 2(-3)^{x}$$
And yes, I forget to mention that x=0 should be the start-point if 2 is included.

tommynaut · Answer

Oops, maybe the "y = " isn't necessary...

kasim17 · Answer

Tommy, if this is for school it would make no sense if they want you to write it all out, and clearly he isn't even paying attention anymore.

whpalmer4 · Answer

If you're trying to write the formula for a geometric series, in my experience that would be
$$a_n = a*r^{n-1}$$where $r$ is the common ratio, $n$ is the number of the term you seek, and $a = a_1$

tommynaut · Answer

I don't think it is for school - I think he just made up some random question. If it was meant to be a geometric series question (which it sort of is) then I think he would have phrased it differently.

whpalmer4 · Answer

If he (or any other reader who stumbles across this question) accidentally learns something by reading it, that isn't all bad, is it? :-)