We need to find the 8th term of the given geometric sequence.
The 8th term of the geometric sequence is -15309.
First term = [tex]a=7[/tex]
Required term = [tex]n=8[/tex]
Common ratio = [tex]r=\dfrac{-21}{7}=\dfrac{63}{-21}=-3[/tex]
The nth term is given by
[tex]a_n=ar^{n-1}\\\Rightarrow a_8=7\times (-3)^{8-1}\\\Rightarrow a_8=7\times (-3)^{7}\\\Rightarrow a_8=-15309[/tex]
Hence, the 8th term of the geometric sequence is -15309.
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