Using arithmetic sequences, it is found that:
a) The sequence is: [tex]a_n = 5 + 3(n - 1)[/tex].
b) 14 blocks will be needed to create the next figure.
c) The sequence means that the number of blocks start at 5 and increase by 3 each figure.
3) The 4th term of the sequence is of -3.
What is an arithmetic sequence?
In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
From the figure, we have that:
- The Figure 3 has 11 dots.
Hence the first term and the common ratio are given as follows:
[tex]a_1 = 5, d = 3[/tex]
The sequence is: [tex]a_n = 5 + 3(n - 1)[/tex], hence the sequence means that the number of blocks start at 5 and increase by 3 each figure.
For item b, the amount is:
[tex]a_4 = 5 + 3(4 - 1) = 14[/tex]
14 blocks will be needed to create the next figure.
For item 3, the sequence is given by:
[tex]a_n = 12 - 5(n - 1)[/tex]
Hence the 4th term is:
[tex]a_4 = 12 - 5(4 - 1) = -3[/tex]
The 4th term of the sequence is of -3.
More can be learned about arithmetic sequences at https://brainly.com/question/6561461
#SPJ1
