{5, 7, 9, 11... 521}

• Define the sequence inthree different ways.

The sequence can be defined in three different ways as:

1. The sequence can be defined by simply listing all the numbers in the sequence like in this case: {5, 7, 9, 11, ..., 521}
2. The sequence can also be defined by an explicit or closed formula which is

an = 2n +5

where n is the position of the number in the sequence and a is the natural number which is part of the list. 5 is the constant which is added in the explicit formula. For instance, to get the number in the third position of the sequence

a3 = (2*3) + 5

which is 11.

Note 5 which is the first value is denoted as a0 and thus 11 is in the third position.

1. A recursive definition may also be used for the sequence. The definition consists a recurrent relation which is relation to previous terms and the initial condition (Levin, 2021).

a0 = 5, an = an-1 + 2

An example solution suing the formula is finding the 4th number in the sequence

A4 = the previous number (a3) +2

A4= 11 +2

=13

Different Sequence

a. 5,8,11,14,17

b. an = a+dn or 5+3n, which is an example of the closedformula. Moreover, the recursive formula would be an = an-5 + d or a=5, an=an-5+3

c. My sequence isarithmetic because it keeps going up by 3 each time, meaning there is exactly 3 between every two points in the set. If my sequence was geometric, the points would need to be changing from each one and not staying constant.

d. The closed formula would be the best option for this sequence because the only variable that changes is the n, which is the number on the steps. It is a quick, fast and efficient way whether you are calculation the 1st step or the 1,000th step.

Question

Is there any pros or cons to one formula over the other?