Geometric Sequence Problem & Solution
(ii) Determine the next four terms of the sequence: \(3, 9, 27, 81, \dots\) (1 mark)
Solution:
Let the terms of the sequence be denoted by \(t_n\).
\(t_1 = 3^1 = 3\)
\(t_2 = 3^2 = 9\)
\(t_3 = 3^3 = 27\)
\(t_4 = 3^4 = 81\)
The general term of this geometric sequence is \(t_n = 3^n\). We need to find the next four terms, which are \(t_5, t_6, t_7, \text{ and } t_8\).
\(t_5 = 3^5 = 243\)
\(t_6 = 3^6 = 729\)
\(t_7 = 3^7 = 2187\)
\(t_8 = 3^8 = 6561\)
\(\therefore\) The next four terms of the sequence are 243, 729, 2187, and 6561.