Question

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 1

`a_n=a_1+(n-1)d\\\\a_1;\ a_2;\ a_3-first\ 3\ terms\ of\ arithmetic\ sequence,\ then\\\\a_2=(a_1+a_3)/(2)\\========================================\\3.)\\a_1=2.1;\ a_2=1.4;\ a_3=0.7\\\\(a_1+a_3)/(2)=(2.1+0.7)/(2)=(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`



`4.)\\a_1=1;\ a_2=1;\ a_3=2;\ a_4=3\\\\(a_1+a_3)/(2)=(1+2)/(2)=(3)/(2)\\eq1=a_2-is\ not\ an\ arithmetic\ sequence`



`5.)\\a_1=0.1;\ a_2=0.3;\ a_3=0.9;\ a_4=2.7\\\\(a_1+a_3)/(2)=(0.1+0.9)/(2)=(1)/(2)\\eq0.3=a_2-is\ not\ an\ arithmetic\ sequence`