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### Question:
Find the next three terms in each sequence. Identify the common difference. Write a recursive function and an explicit function for each sequence.
(The first number is [tex]\( n=1 \)[/tex], not [tex]\( n=0 \)[/tex].)
### 9.
#### a. [tex]\( 3, 7, 11, 15, 19 \)[/tex],
[tex]\[
\qquad \boxed{23}, \boxed{27}, \boxed{31}, \ldots
\][/tex]
#### b. Common Difference:
The common difference ([tex]\( d \)[/tex]) is the difference between consecutive terms in the sequence. To find the common difference:
[tex]\[
d = 7 - 3 = 4
\][/tex]
So, the common difference is [tex]\( \boxed{4} \)[/tex].
#### c. Recursive Function:
The recursive function for this arithmetic sequence is given as:
[tex]\[
a(n) = a(n-1) + 4 \quad \text{with} \quad a(1) = 3
\][/tex]
Thus, the recursive function can be written as:
[tex]\[
\boxed{a(n) = a(n-1) + 4}
\][/tex]
#### d. Explicit Function:
The explicit function for an arithmetic sequence is generally given by:
[tex]\[
a(n) = a(1) + (n-1)d
\][/tex]
For this specific sequence,
[tex]\[
a(n) = 3 + (n-1) \times 4
\][/tex]
So, the explicit function can be written as:
[tex]\[
\boxed{a(n) = 3 + (n-1) \times 4}
\][/tex]
