Question

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17. Write a function rule for the following arithmetic sequence and use it to find the 250th term. Show your work.
−3, 1, 5, 9, ….
Function Rule: Determining 250th term:

Answer 1

First check the difference between terms:

`\{1-(-3),5-1,9-5,\ldots\}=\{4,4,4,\ldots\}`

So every term differs by 4. The first term in the sequence is
`a_1=-3`. Recursively, the sequence is given by

`\begin{cases}a_1=-3\\a_n=a_(n-1)+4&\text{for }n>1\end{cases}`

Then

`a_2=a_1+4`

`a_3=a_2+4=a_1+4(2)`

`a_4=a_3+4=a_1+4(3)`

and so on, with the general rule

`a_n=a_1+4(n-1)\implies a_n=4n-7`

Then the 250th term of the sequence would be

`a_(250)=4(250)-7=993`