Question

Given the explicit formula for an arithmetic sequence find the first five terms and the term named in theproblem.a=65- 100nFind a 39

Answer 1

Given:

a = 65 - 100n

Let's find the first five terms.

`\begin{gathered} \text{First term:} \\ a_1=65-100(1)\text{ = 65-100=-35} \end{gathered}`
`\begin{gathered} \text{Second term:} \\ a_2=65-100(2)=65-200=-135 \end{gathered}`
`\begin{gathered} \text{Third term:} \\ a_3=65-100(3)\text{ = 65 - 300 = }-235 \end{gathered}`
`\begin{gathered} \text{Fourth term:} \\ a_4=65-100(4)\text{ = 65-400=-335} \end{gathered}`
`\begin{gathered} \text{Fifth term:} \\ a_5=65-100(5)=65-500=-435 \end{gathered}`

For a39, we have:

`a_(39)=65-100(39)=65\text{ - 3900=}-3835`

ANSWER:

First term = -35

Second term = -135

Third term = -235

Fourth term = -335

Fifth term = -435

39th term = -3835