Hi Juriemagic,
m∑k=128−k=255.5
First I did a little spreadsheet to see if it worked

You can see that the answer is 9.
Now I will try it without the help of Excel.
The sequence is 128, 64, 32, 16 ,....
This is a GP with r=-0.5 and a=128
Sn=a(1−rn)1−rSn=128(1−(0.5)n)0.5=255.5 256(1−(0.5)n)=255.5 1−(0.5)n=255.5256 1−255.5256=(0.5)n 0.5256=12n 1512=12n 2n=512 n=9
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