Question

Determine if the sequence is arithmetic. If it is, find the common difference.-36,-34, -32, -30, ...оаd=2.OьNot Arithmeticосd = – 2

Answer 1

The sequence is Arithmetic and the common difference is 2

The form of a arithmetic sequence is

`a_n=a_1+(n-1)d`

we know the first term of the sequence: -36. Doing the calculations for a2:

`\begin{gathered} -34=-36+(2-1)d \\ 36-34=2=d \end{gathered}`

The difference between the first and second term is 2. If this is a arithmetic sequence, d has to be the same for all other terms of the sequence.

let's see:

-34+2=-32

-32+2=-30

Thus, the sequence is arithmetic and d=2