Find the first three terms of the arithmetic series. n = 18, an = 112, Sn = 1098?

1 Answer
Jim G.
Aug 8, 2018

#10,16,22#

Explanation:

#"using the n th term and sum to n terms formulae"#

#•color(white)(x)a_n=a_1+(n-1)d#

#•color(white)(x)S_n=n/2[2a_1+(n-1)d]#

#"given "n=18" then"#

#a_(18)=a_1+17d=112to(1)#

#S_(18)=9[2a_1+17d]=1098#

#2a_1+17d=1098/9=122to(2)#

#(2)-(1)rArra_1=10#

#"substitute "a_1=10" in equation "(1)#

#10+17d=112rArrd=102/17=6#

#a_1=10#

#a_2=a_1+d=10+6=16#

#a_3=a_2+d=16+6=22#

#"the first 3 terms are "10,16" and "22#

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