The first five terms and sixth term of the considered pattern is written as: 2, 5, 8, 11, 14, 17
What is arithmetic sequence?
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:
\(a, a + d, a + 2d, ... , a + (n+1)d, ...\)
Its nth term is
\(T_n = a + (n-1)d\)
(for all positive integer values of n)
And thus, the common difference can be obtained as
\(d = T_{n+1} - T_n\)
for any positive integer values of n
For this case, we have:
- Initial term = 2
- Addition of d = 3
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:
\(T_6 = a + (6-1)(d) = 2+(5)(3) = 17\)
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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