A sequence is defined recursively. Write the first five terms.
\[
a_{1}=1 ; \quad a_{n}=4 a_{n-1}
\]
Type the first five terms of the sequence.
\[
a_{1}=\square
\]
Answer
Final Answer: The first five terms of the sequence are \(\boxed{1, 4, 16, 64, 256}\).
Step 1 ：The sequence is defined recursively, which means each term is defined based on the previous term.
Step 2 ：The first term, \(a_1\), is given as 1.
Step 3 ：Each subsequent term, \(a_n\), is defined as 4 times the previous term, \(a_{n-1}\).
Step 4 ：To find the first five terms, we can start with \(a_1\) and use the recursive formula to find \(a_2\), \(a_3\), \(a_4\), and \(a_5\).
Step 5 ：Using the recursive formula, the first five terms of the sequence are 1, 4, 16, 64, 256.
Step 6 ：Final Answer: The first five terms of the sequence are \(\boxed{1, 4, 16, 64, 256}\).
