Question #e6174

1 Answer
Jim G.
Jan 3, 2018

#S_(20)=-400#

Explanation:

#"the terms in the series are the terms of a "color(blue)"arithmetic sequence"#

#a,a+d,a+2d,...a+(n-1)d#

#"where d is the "color(blue)"common difference"#

#d=a_2-a_1=a_3-a_2=.... =a_n-a_(n-1)#

#"here "d=-3-(-1)=-5-(-3)=-2#

#"the sum to n terms of a geometric sequence is"#

#•color(white)(x)S_n=n/2[2a+(n-1)d]#

#"where a is the first term"#

#rArrS_(20)=20/2[(2xx-1)+(-2xx19)]#

#color(white)(xxxx)=10(-2-38)#

#color(white)(xxxx)=10xx-40=-400#

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