Question

What is the type of sequence and the he common difference/ratio

Answer 1

We have a sequence:

`-(11)/(4),-2,-(5)/(4),-(1)/(2),(1)/(4)`

If the sequence is arithmetic, we will have a common difference between the terms. That is that the difference between consecutive terms has a constant value for all pair of consecutive terms.

We can check if there is a constant difference as:

`a_2-a_1=-2-(-(11)/(4))=-(8)/(4)+(11)/(4)=(3)/(4)`
`a_3-a_2=-(5)/(4)-(-2)=-(5)/(4)+(8)/(4)=(3)/(4)`

It seems that we may have common difference, but to be sure we have to check for all pair of terms as one pair that does not have the same difference will make the sequence to not be arithmetic.

We then continue checking with the other terms:

`\begin{gathered} a_4-a_3=-(1)/(2)-(-(5)/(4))=-(2)/(4)+(5)/(4)=(3)/(4) \\ \\ a_5-a_4=(1)/(4)-(-(1)/(2))=(1)/(4)+(2)/(4)=(3)/(4) \end{gathered}`

Then, we have checked that this sequence is aritgmetic with a common difference of 3/4.

Answer:

Type of sequence: Arithmetic

Common difference: 3/4