+0  
 
+1
183
2
avatar+1442 

The sum of the first n terms in the infinite geometric sequence {1/4, 1/8, 1/16, ...} is 255/512. Find n.

 

👍 👍 

AnonymousConfusedGuy  Jan 16, 2018
 #1
avatar+89803 
+1

The common ratio, r,  can be determined  as  the ratio of the terms

 

an+1  / an    so we have....  (1/8)  / (1/4)   =  4/8  =  1/2

 

And we have that

 

255/512  =  1/4  [  1 -  (1/2)^n ] /  [  1  - 1/2  ]

 

255/512 =   1/4   [ 1 - (1/2)^n ]  /  (1/2)

 

255/512  =  (1/2)  [ 1 - (1/2)^n ]     multiply both sdes by  2

 

255* 2 / 512   =  1 - (1/2)^n  rearrange  as

 

(1/2)^n  =  1  -  510/512

 

(1/2)^n   =  [ 512  - 510 ] / 512    =  2 / 512  =   1/256

 

Take the log of both sides

 

log (1/2)^n  =  log (1/256)     and we can write

 

n  =  log (1/256) / log (1/2)

 

n  =   8    ⇒  8 terms

 

 

cool cool cool

CPhill  Jan 16, 2018
 #2
avatar+1442 
+2

Thanks so much!

AnonymousConfusedGuy  Jan 16, 2018

23 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.