Decide whether the sequence can be represented perfectly by a linear or a quadratic model. If so, then find the...

Firstly we need to determine whether the series is linear or quadratic. A linear sequence is a sequence of numbers in which there is a first difference between any consecutive terms is constant. However, a quadratic sequence is a sequence of numbers in which there is a second difference between any consecutive terms is constant. 

Let's determine if the above sequence has a first difference: 

From above we observe there is no first difference, now let's determine the second difference: 

From above we observe that the second difference is constant. Therefore the sequence is perfectly quadratic.

Let's determine the quadratic model using the following formula: 

where: T_n = term value, ,n = term, variables: a,b,c

 = second difference

Let's find variable b: 

  first difference between term 2 and term 1

 (substitute for a and first difference between term 2 and term1)

Lastly we are finding variable c: 

 value of term 1

 (substitute for a, b and value of term 1

Now we have determined the variables, we can develop our model: 

Let's double check our formula using term 4: 

SUMMARY: 

Sequence: Quadratic

Model: 

• Next Do you think the KKK is a terrorist group?
• Previous Why has no one told Bruno the reason for the concentration camp, and why does Bruno's family not realize that he is gone and, then, see him among...