Question

Sequences are functions. The key here is that the input is simply the number's place in line so to speak and

the output is the actual number in the list.
Exercise #2: Consider the sequence defined by the formula a(n) = 2n+1.
(a) Write out the first 5 elements of this sequence.
an=2n+1.
9=3
9₂=5
b) Graph the sequence on the grid shown below for 1≤n≤5.
c) Why shouldn't we connect the points plotted with a continuous straight line?
) What is the 21st term of this sequence? Show how you arrived
at your answer.
a(n)
n

Answer 1

The first 5 elements of the sequence a(n) = 2n + 1 are 3, 5, 7, 9, and 11. We should not connect the points on the graph with a straight line because the sequence is discrete. The 21st term of the sequence is 43.

Step-by-step explanation:

The sequence defined by the formula a(n) = 2n + 1 is a list of numbers generated by substituting the term number (n) into the formula to find the value of the term (a(n)). To write out the first 5 elements of this sequence, we substitute the values 1 through 5 for n into the equation:
a(1) = 2(1) + 1 = 3

a(2) = 2(2) + 1 = 5

a(3) = 2(3) + 1 = 7

a(4) = 2(4) + 1 = 9

a(5) = 2(5) + 1 = 11

Graphing the sequence for 1≤n≤5 would involve plotting the points (1,3), (2,5), (3,7), (4,9), and (5,11) on the coordinate plane. However, we shouldn't connect the points with a continuous line because the sequence is discrete: each term corresponds to a specific natural number, and there are no 'in-between' values An example of visualizing this is picturing a scatter plot instead of a line graph.

To find the 21st term of the sequence, we use the formula:

a(21) = 2(21) + 1

= 42 + 1

= 43

So, the 21st term of the sequence is 43.