Sure, let's find the first four terms of the sequence given by the recursive formula [tex]\( a_n = 3a_{n-1} \)[/tex] with the initial term [tex]\( a_1 = 6 \)[/tex].
1. First term:
- We are given [tex]\( a_1 = 6 \)[/tex].
2. Second term:
- To find the second term [tex]\( a_2 \)[/tex], we use the formula [tex]\( a_n = 3a_{n-1} \)[/tex] for [tex]\( n = 2 \)[/tex].
[tex]\[
a_2 = 3a_1 = 3 \times 6 = 18
\][/tex]
3. Third term:
- To find the third term [tex]\( a_3 \)[/tex], we use the formula [tex]\( a_n = 3a_{n-1} \)[/tex] for [tex]\( n = 3 \)[/tex].
[tex]\[
a_3 = 3a_2 = 3 \times 18 = 54
\][/tex]
4. Fourth term:
- To find the fourth term [tex]\( a_4 \)[/tex], we again use the formula [tex]\( a_n = 3a_{n-1} \)[/tex] for [tex]\( n = 4 \)[/tex].
[tex]\[
a_4 = 3a_3 = 3 \times 54 = 162
\][/tex]
So, the first four terms of the sequence are [tex]\( 6 \)[/tex], [tex]\( 18 \)[/tex], [tex]\( 54 \)[/tex], and [tex]\( 162 \)[/tex].
