Respuesta :
We have to find the 99th term of the arithmetic sequence: 2,-3, -8...
First, we have to find the explicit function for this arithmetic sequence.
This mean that we have to find the common difference for this sequence:
[tex]\begin{gathered} a_2=a_1+d \\ -3=2_{}+d\Rightarrow d=-3-2=-5 \\ a_3=a_2+d \\ -8=-3+d\Rightarrow d=-8+3=-5 \end{gathered}[/tex]The common difference is d = -5.
We now can find the expression for the explicit function for this sequence as:
[tex]\begin{gathered} a_2=a_1-5 \\ a_3=a_2-5=(a_1-5)-5=a_1+2(-5) \\ a_4=a_3-5=a_1+3(-5) \\ a_n=a_1+(n-1)(-5) \\ a_n=2+(n-1)(-5) \end{gathered}[/tex]Then, we can find the 99th term by calculating this formula for n = 99:
[tex]\begin{gathered} a_{99}=2+(99-1)(-5) \\ a_{99}=2+98(-5) \\ a_{99}=2-490 \\ a_{99}=-488 \end{gathered}[/tex]Answer: the 99th of this sequence is -488.
