Respuesta :
The nth term rule of the given quadratic sequence is [tex]a_{n} = a_{n-1} + 2n-3[/tex]
Determining nth term
From the question, we are to determine the nth term rule of the given sequence.
The given sequence is
− 5 , − 4 , − 1 , 4 , 11 , 20 , 31 , . . .
From the above sequence, we can observe that a term is determine by adding 1 less twice the position of the previous term to the sum of the previous term
That is,
[tex]a_{n} = a_{n-1} + 2(n-1) -1[/tex]
This can be simplified into
[tex]a_{n} = a_{n-1} + 2n-2 -1[/tex]
[tex]a_{n} = a_{n-1} + 2n-3[/tex]
Hence, the nth term rule of the given quadratic sequence is [tex]a_{n} = a_{n-1} + 2n-3[/tex]
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