Answer:
Step-by-step explanation:
Given: The firs term of the pattern = 2
The common difference between the term d= 3
Therefore, the next term of the pattern will be =
The first five terms and sixth term of the considered pattern is written as: 2, 5, 8, 11, 14, 17
An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
[tex]a, a + d, a + 2d, ... , a + (n+1)d, ...[/tex]
Its nth term is
[tex]T_n = a + (n-1)d[/tex]
(for all positive integer values of n)
And thus, the common difference can be obtained as
[tex]d = T_{n+1} - T_n[/tex]
for any positive integer values of n
For this case, we have:
Thus, we get the sequence's first five terms as:
2, 2+3, 2+3+3, 2+3+3+3, 2+3+3+3+3
or 2, 5, 8, 11, 14
For sixth term, we get its expression as:
[tex]T_6 = a + (6-1)(d) = 2+(5)(3) = 17[/tex]
Thus, the first five terms and sixth term of the considered pattern is written as: 2, 5, 8, 11, 14, 17
Learn more about arithmetic sequence here;
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