Question

Calculateas?for the sequence {an}{.)={4,-2-3-2.0.Ο Α. 78OB. 1592O C. 81OD. 1712

Answer 1

Given:

`\mleft\lbrace-6,-(9)/(2),-3,-(3)/(2),0,\ldots\mright\rbrace`

Given sequence is an Ap sequence

`\begin{gathered} d=-(9)/(2)-(-6) \\ d=-(9)/(2)+6 \\ d=(3)/(2) \end{gathered}`
`a=-6`
`\begin{gathered} a_n=a+(n-1)d \\ a_n=-6+(n-1)((3)/(2)) \end{gathered}`
`\begin{gathered} a_(57)=-6+56((3)/(2)) \\ a_(57)=-6+28(3) \\ a_(57)=-6+84 \\ a_(57)=78 \end{gathered}`

Option A is the final answer.