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Determine whether each sequence appears to be an arithmetic sequence. If so find the common difference and the next 3 terms.

3.) 2.1, 1.4, 0.7, 0,...
4.) 1, 1, 2, 3...
5.) 0.1, 0.3, 0.9, 2.7...



Answer :

[tex]a_n=a_1+(n-1)d\\\\a_1;\ a_2;\ a_3-first\ 3\ terms\ of\ arithmetic\ sequence,\ then\\\\a_2=\frac{a_1+a_3}{2}\\========================================\\3.)\\a_1=2.1;\ a_2=1.4;\ a_3=0.7\\\\\frac{a_1+a_3}{2}=\frac{2.1+0.7}{2}=\frac{2.8}{2}=1.4=a_2\ \ \ O.K. :)\\\\d=a_2-a_1\to d=1.4-2.1=-0.7\\\\a_4=0\to a_5=a_4+d\to a_5=0+(-0.7)=-0.7\\\\a_6=-0.7+(-0.7)=-1.4\\\\a_7=-1.4+(-0.7)=-2.1[/tex]


[tex]4.)\\a_1=1;\ a_2=1;\ a_3=2;\ a_4=3\\\\\frac{a_1+a_3}{2}=\frac{1+2}{2}=\frac{3}{2}\neq1=a_2-is\ not\ an\ arithmetic\ sequence[/tex]


[tex]5.)\\a_1=0.1;\ a_2=0.3;\ a_3=0.9;\ a_4=2.7\\\\\frac{a_1+a_3}{2}=\frac{0.1+0.9}{2}=\frac{1}{2}\neq0.3=a_2-is\ not\ an\ arithmetic\ sequence[/tex]

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