Question #e6469

1 Answer
Jim G.
Feb 3, 2018

#S_(10)=165#

Explanation:

#"using the formula related to "color(blue)"arithmetic sequences"#

#•color(white)(x)a_n=a+(n-1)dlarrcolor(blue)"nth term"#

#•color(white)(x)S_n=n/2[2a+(n-1)d]larrcolor(blue)"sum to n terms"#

#"before we can calculate the sum of 10 terms we require"#
#"the values of a and d"#

#S_3=a+a+d+a+2d=18#

#rArr3a+3d=18to(1)#

#"in the same way the sum of terms 8, 9 and 10 is"#

#a+7d+a+8d+a+9d=81#

#rArr3a+24d=81to(2)#

#(2)-(1)" term by term eliminates a"#

#rArr21d=63rArrd=3#

#"substitute "d=3" in equation "(1)#

#3a+9=18#

#rArr3a=9rArra=3#

#rArrS_(10)=10/2[(2xx3)+(9xx3)]#

#color(white)(rArrS_(10))=5xx33=165#

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