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the first term of a geometric series is 1,the nth term is 128 and the sum of the n terms is 256 find the common ratio and the number of terms.

Guest Jul 4, 2017
 #1
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lets call the ratio q, ok?

 

the sum of the first term+the second term+.....+the nth term=a1*(qn-1)/(q-1). a1=1, so the sum=(qn-1)/(q-1). we know the nth term is 128, so qn-1=128, so qn=128*q

 

128*q-1/q-1=256

 

 

128*q-1=256*q-256

 

 

-1=128*q-256

 

128*q=255

 

q=255/128

 

the series is impossible

Guest Jul 4, 2017
 #2
avatar+27052 
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I suspect the sum should be 255, rather than 256. If so everything works out nicely!

Alan  Jul 4, 2017

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