To find [tex]\( a_4 \)[/tex] using the given recursive formula [tex]\( a_n = 3a_{n-1} - 10 \)[/tex] with the initial term [tex]\( a_1 = 7 \)[/tex], we will calculate the terms of the sequence step-by-step.
1. Calculate [tex]\( a_2 \)[/tex]
[tex]\[
a_2 = 3a_1 - 10
\][/tex]
Substitute [tex]\( a_1 = 7 \)[/tex]:
[tex]\[
a_2 = 3 \times 7 - 10 = 21 - 10 = 11
\][/tex]
2. Calculate [tex]\( a_3 \)[/tex]
[tex]\[
a_3 = 3a_2 - 10
\][/tex]
Substitute [tex]\( a_2 = 11 \)[/tex]:
[tex]\[
a_3 = 3 \times 11 - 10 = 33 - 10 = 23
\][/tex]
3. Calculate [tex]\( a_4 \)[/tex]
[tex]\[
a_4 = 3a_3 - 10
\][/tex]
Substitute [tex]\( a_3 = 23 \)[/tex]:
[tex]\[
a_4 = 3 \times 23 - 10 = 69 - 10 = 59
\][/tex]
Therefore, the value of [tex]\( a_4 \)[/tex] is [tex]\( \boxed{59} \)[/tex].
