What is the 7th term of the geometric sequence where a1 = -625 and a2 = 125?

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Answer 1 · 2015-07-17T23:36:15

The seventh term of the sequence is #color(red)(-1/25)#.

We first find the common ratio #r# by dividing a term by its preceding term.

#r = a_2/a_1 = 125/(-625)#

#r = -1/5#

Now we use the #n^"th"# term rule:

#t_n = ar^(n-1)#, where #a# is the first term and #r# is the common ratio

#t_7 = -625(-1/5)^(7-1) = -625(-1/5)^6 = -(5^4)(-1)^6/5^6 = -(5^4 × 1)/5^6 = -5^4/5^6 = -1/5^2#

#t_7 = -1/25#