The 5th term of a geometric sequence is 45 and the 8th term is 360. How do you determine the 20th term?

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Answer 1 · 2016-02-17T14:36:48

#1474560#

First we need to find the ratio, #r# and the first term:#a#.
We know that #a*r^5=45# and #a*r^8=360#.

To determine #r# can divide the 8th term by the 5th term like so:

#(ar^8)/(ar^5)=360/45#

The #a#s will cancel and the rest will simplify to:

#r^3=8#
#-> r =2#

To find #a# simply substitute #r# into either of the known terms, i.e:

#a*2^5=45-> a=45/2^5=45/32#

Now we can find the twentieth term:

#ar^20=45/32*2^20=1474560#