The summation notation for the given series is [tex]\sum_{n=1}^{12}(2.5-1.5n)[/tex]
The given series is,
[tex]1,-0.5,-2,........[/tex]
Since, [tex]-0.5-1=-2+0.5=-1.5[/tex]
Here we observe that, common difference between each term is - 1.5.
So, given series is an Arithmetic progression series.
First term, [tex]a=1[/tex], common difference, [tex]d=-1.5[/tex]
General term for AP series,
[tex]a_{n}=a+(n-1)d\\\\a_{n}=1+(n-1)*(-1.5)\\\\a_{n}=1-1.5n+1.5\\\\a_{n}=2.5-1.5n[/tex]
Hence, summation series up to 12 terms is,
[tex]\sum_{n=1}^{12}(2.5-1.5n)[/tex]
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