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The first term of a geometric series is 2, the nth term is 486 and the sum of the n terms is 728. Find r and n

 Aug 24, 2015

Best Answer 

 #1
avatar+26396 
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The first term of a geometric series is 2, the nth term is 486 and the sum of the n terms is 728.

Find r and n

 

(1)a1=a=2(2)an=arn1486=2rn1rn1=243(3)snsn1=an728sn1=486sn1=728486sn1=242(4)sn1=arn11r1242=22431r1242=2242r1r1=2r=3(5)rn1=2433n1=35n1=5n=6

 

r = 3 and n = 6

 

geometric sequence: a1=230=2a2=231=6a3=232=18a4=233=54a5=234=162a6=235=486s6=728 

 

check:

an=a6=235=486( okay)

 

 Aug 24, 2015
 #1
avatar+26396 
+5
Best Answer

The first term of a geometric series is 2, the nth term is 486 and the sum of the n terms is 728.

Find r and n

 

(1)a1=a=2(2)an=arn1486=2rn1rn1=243(3)snsn1=an728sn1=486sn1=728486sn1=242(4)sn1=arn11r1242=22431r1242=2242r1r1=2r=3(5)rn1=2433n1=35n1=5n=6

 

r = 3 and n = 6

 

geometric sequence: a1=230=2a2=231=6a3=232=18a4=233=54a5=234=162a6=235=486s6=728 

 

check:

an=a6=235=486( okay)

 

heureka Aug 24, 2015

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