Let's start with the given recursive formula for the sequence:
[tex]\[
f(n) = \begin{cases}
f(1) = 6 \\
f(n) = f(n-1) + 7 \text{ if } n > 1
\end{cases}
\][/tex]
To find the first 4 terms of the sequence, we will calculate each term step-by-step:
1. First term [tex]\( f(1) \)[/tex]:
[tex]\[
f(1) = 6
\][/tex]
So, the first term [tex]\( f(1) \)[/tex] is 6.
2. Second term [tex]\( f(2) \)[/tex]:
[tex]\[
f(2) = f(1) + 7 = 6 + 7 = 13
\][/tex]
So, the second term [tex]\( f(2) \)[/tex] is 13.
3. Third term [tex]\( f(3) \)[/tex]:
[tex]\[
f(3) = f(2) + 7 = 13 + 7 = 20
\][/tex]
So, the third term [tex]\( f(3) \)[/tex] is 20.
4. Fourth term [tex]\( f(4) \)[/tex]:
[tex]\[
f(4) = f(3) + 7 = 20 + 7 = 27
\][/tex]
So, the fourth term [tex]\( f(4) \)[/tex] is 27.
Therefore, the first 4 terms of the sequence are: [tex]\( 6, 13, 20, 27 \)[/tex].
