Respuesta :

LammettHash
Recursively, this sequence is given by

[tex]\begin{cases}a_1=-13\\a_n=a_{n-1}-4&\text{for }n>1\end{cases}[/tex]

You can solve for the [tex]n[/tex]th term explicitly:

[tex]a_n=a_{n-1}-4=a_{n-2}-2\times4=a_{n-3}-3\times4=\cdots=a_1-(n-1)\times4[/tex]

So the explicit formula for this sequence would be

[tex]a_n=-13-4(n-1)=-4n-9[/tex]

This means the 41st term is

[tex]a_{41}=-4(41-1)-9=-173[/tex]

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