Respuesta :
[tex]\operatorname{Re}cursive\colon a_n=a_{n-1}+6[/tex]
see explanation below
Explanation:8) 3, 9, 15, 21, 27
The common difference = 15-9 = 9-3
The common difference = d = 6
Hence, it is an arithmetric sequence
The recursive formula:
[tex]\begin{gathered} a_{n+1}=a_n+\text{ 6} \\ \text{OR} \\ a_n=a_{n-1}+\text{ d} \\ a_n=a_{n-1}+6 \end{gathered}[/tex]The appropriate formula:
[tex]\begin{gathered} a_n=a_1+\text{ (n-1)d} \\ \text{where a}_1\text{ = }3\text{ } \\ a_n=3_{}+\text{ (n-1)d} \end{gathered}[/tex]The next three numbers in the sequence:
[tex]\begin{gathered} \text{The last term in the sequence given was 6th term. } \\ \text{The next }3\text{ terms will be: 7th, 8th and 9th term} \end{gathered}[/tex][tex]\begin{gathered} a_7\text{ = 3 + (7-1)}\times6 \\ =\text{ 3+ (6)(6) = 3 + 36} \\ 7th\text{ term = }a_7=39 \end{gathered}[/tex][tex]\begin{gathered} a_8\text{ = 3 + (8-1)}\times6 \\ =\text{ 3+ (7)(6) = 3 + 4}2 \\ 8th\text{ term = }a_8\text{ =}45 \end{gathered}[/tex][tex]\begin{gathered} a_9\text{ = 3 + (9-1)}\times6 \\ a_9\text{ = }3\text{ + 8(6) = 3 + 48} \\ 9th\text{ term = }51 \\ \end{gathered}[/tex]