Question

Find S15 for the series -1 + -3 + -5 + -7 +...

Answer 1

The given series is $-1 + -3 + -5 + -7 +...$

Alternatively it can be written as , say s then

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