Question

Find the tenth term in each sequence. -1,2/3,7/3,4,17/3

Answer 1

It'a an arithmetic sequence:

`a_1=-1\\\\a_2=-1+(5)/(3)=-(3)/(3)+(5)/(3)=(2)/(3)\\\\a_3=(2)/(3)+(5)/(3)=(7)/(3)\\\\a_4=(7)/(3)+(5)/(3)=(12)/(3)=4\\\\a_5=4+(5)/(3)=(12)/(3)+(5)/(3)=(17)/(3)\\\vdots\\\\\text{The general formula for nth term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\\\\\text{We have}\ a_1=-1\ \text{and}\ d=(5)/(3).\\\\\text{Substitute}\\\\a_n=-1+(n-1)\left((5)/(3)\right)=-1+(5)/(3)n-(5)/(3)=(5)/(3)n-(3)/(3)-(5)/(3)`

`\boxed{a_n=(5)/(3)n-(8)/(3)}`