Respuesta :

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]

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