What is the 9th term of the geometric sequence where a1 = -8 and a6 = -8,192?

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Answer 1 · 2016-05-31T18:23:01

We must first find the common ratio #r#.

The #nth# term of a geometric series is given by #t_n = a xx r^(n - 1)#. We know #a#, the first term, we know #t_6#, and therefore we know #n (6)#

#-8192 = -8 xx r^(6 - 1)#

#-8192/-8 = r^5#

#1024 = r^5#

#root(5)(1024) = r#

#4 = r#

Now, we can reuse the formula #t_n = a xx r^(n - 1)# to find the 9th term.

#t_9 = -8 xx 4^(9 - 1)#

#t_9 = -8 xx 4^8#

#t_9 = -524288#

Therefore, #t_9# is -524 288.

Practice exercises:

Determine the 11th term of a geometric sequence where the first term is 27 and #t_4# is 1.
Determine the 7th term of a geometric sequence where the second term is 3 and the fifth is 375.

Hopefully this helps, and Good luck!