The third term of an Arithmetic Sequence is -12 and the seventh term is 8. what is the sum of the first 10 terms?

1 Answer
Jim G.
Jun 23, 2018

#S_(10)=5#

Explanation:

#"using the nth term expression and the sum to n terms of"#
#"an arithmetic sequence"#

#•color(white)(x)a_n=a+(n-1)d#

#•color(white)(x)S_n=n/2[2a+(n-1)d]#

#"we require to find a and d"#

#a_3=-12" and "a_7=8" thus"#

#a+2d=-12to(1)#

#a+6d=8to(2)#

#(2)-(1)" gives"#

#4d=20rArrd=5#

#"substitute in equation "(1)#

#a+10=-12rArra=-22#

#rArrS_(10)=10/2[(2xx-22)+(9xx5)]#

#color(white)(rArrS_(10))=5(-44+45)=5#

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