0,0,-1,-3,-7.5,-12,-17.5,-24,-31.5,-40,-49.5,-60,-71.5,-84,-97.5,-112,-127.5,-144,-161.5,-180
#what is the general rule for this pattern
lost wigeon
vagrant martenBOT
lost wigeon
<@&286206848099549185> need some help here
south fog
where did this sequence come from?
lost wigeon
I toke T(n)=a+(n-1)d then I started n at 1 a and d started at zero then each time n increase by 1 a increases by a half and d decreases by a half
That's how I got the sequence @south fog
south fog
so $T_n = a_n + (n - 1)d_n$, and $a_0 = d_0 = 0$, and $a_n$ and $d_n$ each themselves form an AP with common difference $\pm \frac12$ respectively.
spiral talonBOT
Ann
south fog
which means $T_n = \frac{1}{2}n - \frac{1}{2}n(n-1)$ directly from the definition that you just told me, i think.
spiral talonBOT
Ann
lost wigeon
Let me test it
It doesn't work
As if you use that version n=1 is 1/2 which Is not true as n=1 is 0
You try it
@south fog
south fog
and you are certain that you did not miscalculate anything at any point?
do you have your work written down so i can take a look
lost wigeon
I don't have my work but I didn't miss caculate
But I can try showing you first few terms and how I got them
south fog
sure
south fog
oh, my indexing was off.
so then $a_n = \frac{1}{2} (n-1)$ and $d_n = -\frac{1}{2} (n-1)$.
spiral talonBOT
Ann
south fog
and, still according to the very same definition that you gave, you were calculating $$T(n) = \frac{1}{2} (n-1) - \frac{1}{2} (n-1)^2.$$
spiral talonBOT
Ann
south fog
which can be simplified a bit, i guess.
i thought $a_0 = d_0 = 0$ but actually it was $a_1 = d_1 = 0$.
spiral talonBOT
Ann
south fog
you still were specifying your sequence by means of a formula.
lost wigeon
and, still according to the very same definition that you gave, you were calcula...
Thanks for the help
south fog
!done @lost wigeon
vagrant martenBOT
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