Is the sequence #1/3, 0, 1, -2# arithmetic, geometric, or neither?

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Answer 1 · 2017-11-02T17:43:06

nether a GP nor an AP

#1/3,0,1,-2#

#(a)# check for AP

for an AP there is a common difference between the terms

#d=u_(n+1)-u_n#

#u_2-u_1=0-1/3=-1/3#

#u_3-u_2=1-0=1#

not the same difference therefore not an AP

#(b) #check for GP

for a GP there is a common ratio between terms

#r=(u_(n+1))/u_n#

#u_2/u_1=0/(1/3)=0#

a common ratio of zero doesn't give a GP