Respuesta :
we are given
geometric sequence -36, 6, -1, 1/6, ...
first term is -36
[tex] a_1=-36 [/tex]
now, we can find common ratio
[tex] r=\frac{6}{-36} [/tex]
[tex] r=-\frac{1}{6} [/tex]
now, we can find nth term
[tex] a_n=a_1(r)^{n-1} [/tex]
now, we can plug values
and we get
[tex] a_n=36(-\frac{1}{6})^{n-1} [/tex]
now, we can find 5th term , 6th term, 7th term
fifth term:
[tex] a_5=36(-\frac{1}{6})^{4} [/tex]
[tex] a_5=\frac{1}{36} [/tex]
sixth term:
[tex] a_6=36(-\frac{1}{6})^{5} [/tex]
[tex] a_6=-\frac{1}{216} [/tex]
seventh term:
[tex] a_7=36(-\frac{1}{6})^{6} [/tex]
[tex] a_7=\frac{1}{1296} [/tex]
so, next terms are
[tex] a_5=\frac{1}{36} [/tex] , [tex] a_6=-\frac{1}{216} [/tex]
, [tex] a_7=\frac{1}{1296} [/tex].............Answer
