The given series is [tex] -1 + -3 + -5 + -7 +... [/tex]
Alternatively it can be written as , say s then
[tex] S= -1 -3 -5 -7 ...\\
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S=-(1+3+5+7+........)\\
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\text{This is an arithmetic series with first term=a=1 and }\\
\text{common diffrence=d=3-1=2}\\
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\text{Using the arithmetic series sum formula we can say}\\
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S_n=\frac{n}{2}[2a+(n-1)d]\\
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S_{15}=\frac{15}{2}[2*1+(15-1)*2]\\
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S_{15}=\frac{15}{2}[2+28]\\
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S_{15}=\frac{15}{2}*30\\
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S_{15}=225\\
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\text{Hence the sum of the given sequence is }= -225\\ [/tex]
