ExplanationThe sequence \(S_n = 2(S_{n - 1}) - 4\) can be read as “to get any term in sequence S, double the previous term and subtract 4.”
The problem gives \(S_1\) (the first term) and asks for \(S_5\) (the fifth term):
6 | | | | |
\(S_1\) | \(S_2\) | \(S_3\) | \(S_4\) | \(S_5\) |
To get any term, double the previous term and subtract 4. To get \(S_2\), double \(S_1\) (which is 6) and subtract 4: \(S_2 = 2(6) - 4 = 8\).
Continue doubling each term and subtracting 4 to get the subsequent term:
6 | 8 | 12 | 20 | 36 |
\(S_1\) | \(S_2\) | \(S_3\) | \(S_4\) | \(S_5\) |