Let's find the first 4 terms for each sequence provided:
### Part a) [tex]\(a_n = n + 4\)[/tex]
To find the first 4 terms, we will substitute [tex]\( n = 1, 2, 3, 4 \)[/tex] into the given formula [tex]\(a_n = n + 4\)[/tex].
1. For [tex]\( n = 1 \)[/tex]:
[tex]\[
a_1 = 1 + 4 = 5
\][/tex]
2. For [tex]\( n = 2 \)[/tex]:
[tex]\[
a_2 = 2 + 4 = 6
\][/tex]
3. For [tex]\( n = 3 \)[/tex]:
[tex]\[
a_3 = 3 + 4 = 7
\][/tex]
4. For [tex]\( n = 4 \)[/tex]:
[tex]\[
a_4 = 4 + 4 = 8
\][/tex]
Thus, the first 4 terms of the sequence [tex]\(a_n = n + 4\)[/tex] are:
[tex]\[
[5, 6, 7, 8]
\][/tex]
### Part b) [tex]\(a_n = 12 - 3n\)[/tex]
To find the first 4 terms, we will substitute [tex]\( n = 1, 2, 3, 4 \)[/tex] into the given formula [tex]\(a_n = 12 - 3n\)[/tex].
1. For [tex]\( n = 1 \)[/tex]:
[tex]\[
a_1 = 12 - 3 \cdot 1 = 12 - 3 = 9
\][/tex]
2. For [tex]\( n = 2 \)[/tex]:
[tex]\[
a_2 = 12 - 3 \cdot 2 = 12 - 6 = 6
\][/tex]
3. For [tex]\( n = 3 \)[/tex]:
[tex]\[
a_3 = 12 - 3 \cdot 3 = 12 - 9 = 3
\][/tex]
4. For [tex]\( n = 4 \)[/tex]:
[tex]\[
a_4 = 12 - 3 \cdot 4 = 12 - 12 = 0
\][/tex]
Thus, the first 4 terms of the sequence [tex]\(a_n = 12 - 3n\)[/tex] are:
[tex]\[
[9, 6, 3, 0]
\][/tex]
In summary, for the given sequences:
a) The first 4 terms of [tex]\(a_n = n + 4\)[/tex] are [tex]\([5, 6, 7, 8]\)[/tex].
b) The first 4 terms of [tex]\(a_n = 12 - 3n\)[/tex] are [tex]\([9, 6, 3, 0]\)[/tex].
