Answer:
[tex]T_n = T_{n-1} + 11[/tex]
[tex]T_1 = -8[/tex]
Step-by-step explanation:
Given
[tex]-8, 3, 14, 25,...[/tex]
Required
The recursive function
Let the nth term of the sequence be [tex]T_n[/tex]
The given sequence is an arithmetic sequence that has the following common difference (d)
[tex]d = T_2 - T_1[/tex]
[tex]d = 3--8[/tex]
[tex]d =11[/tex]
So, the nth term is:
[tex]T_n = T_{n-1} + d[/tex]
[tex]T_n = T_{n-1} + 11[/tex]
Hence, the recursion is:
[tex]T_n = T_{n-1} + 11[/tex] where [tex]T_1 = -8[/tex]
