To solve this problem, let's step through the sequence using the given recurrence relation and the initial term.
1. We are given the initial term [tex]\( u_1 = -2 \)[/tex].
2. To find [tex]\( u_2 \)[/tex]:
[tex]\[
u_2 = 3 \cdot u_1 + 7
\][/tex]
Plugging in the value of [tex]\( u_1 \)[/tex]:
[tex]\[
u_2 = 3 \cdot (-2) + 7 = -6 + 7 = 1
\][/tex]
3. Next, we determine [tex]\( u_3 \)[/tex]:
[tex]\[
u_3 = 3 \cdot u_2 + 7
\][/tex]
Using the value found for [tex]\( u_2 \)[/tex]:
[tex]\[
u_3 = 3 \cdot 1 + 7 = 3 + 7 = 10
\][/tex]
Thus, the values are:
[tex]\[
u_2 = 1, \quad u_3 = 10
\][/tex]
