How do you find the 7th term of the geometric sequence with the given terms a4 = 54, a5 = 162?

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Answer 1 · 2016-01-20T03:23:37

#a_7 = 1458#

Since this is a geometric sequence we know the following

#a_n= a_1r^(n-1)# noticed we started at 1 that why we subtract 1 from n

the ratio #r = (a_n)/(a_(n-1))#

We are given

#a_4 =54 " " " a_5= 162#

We first, need to find #r#

#r= (a_5)/(a_4) = 162/54 = 3#

Then we can use the formula #a_n = a_1r^(n-1) #

(but instead of finding #a_1# , we will use #a_4# we need to subtract 4 from the nth term

#a_7= a_4r^(7-4)#

#a_7 = (54)(3)^(3)#

#" a_7 = 1458#