Solution Step-by-Step
(vii) 2, 5, 8, 11, .... (1 mark)
\(t_1 = 2\)
\(t_2 = 2 + 3 = 5\)
\(t_3 = 5 + 3 = 8\)
\(t_4 = 8 + 3 = 11\)
To find the next four terms, we continue adding the common difference (3) to the previous term:
\(t_5 = 11 + 3 = 14\)
\(t_6 = 14 + 3 = 17\)
\(t_7 = 17 + 3 = 20\)
\(t_8 = 20 + 3 = 23\)
\(\therefore\) The next four terms of the sequence are 14, 17, 20 and 23.
Additional Practice Examples
Example 1: Constant Addition
Find the next three terms of the sequence: 4, 9, 14, 19, ...
Pedagogical Hint: First, identify the difference between consecutive terms. \(9 - 4 = 5\) and \(14 - 9 = 5\). The common difference is 5.
\(t_1 = 4\)
\(t_2 = 4 + 5 = 9\)
\(t_3 = 9 + 5 = 14\)
\(t_4 = 14 + 5 = 19\)
Now, calculate the subsequent terms:
\(t_5 = 19 + 5 = 24\)
\(t_6 = 24 + 5 = 29\)
\(t_7 = 29 + 5 = 34\)
\(\therefore\) The next three terms are 24, 29, and 34.
Example 2: Decreasing Sequence
Find the next three terms of the sequence: 20, 17, 14, 11, ...
Pedagogical Hint: Notice the numbers are getting smaller. The difference is negative. \(17 - 20 = -3\).
\(t_1 = 20\)
\(t_2 = 20 - 3 = 17\)
\(t_3 = 17 - 3 = 14\)
\(t_4 = 14 - 3 = 11\)
Continuing the pattern by subtracting 3:
\(t_5 = 11 - 3 = 8\)
\(t_6 = 8 - 3 = 5\)
\(t_7 = 5 - 3 = 2\)
\(\therefore\) The next three terms are 8, 5, and 2.