My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 15th, 2006, 01:34 PM   #1
Newbie
 
Joined: Dec 2006

Posts: 28
Thanks: 0

Term of the geometric

Find the sum of the first 10 terms of the geometric series whose first term is -6 and whose common ratio is -2
Sean is offline  
 
December 15th, 2006, 04:57 PM   #2
Guest
 
Joined:

Posts: n/a
Thanks:

Why can't you just use the formula for a geometric series?:

a/(1-r)


(-6)/(1-(-2))=-2
 
December 16th, 2006, 03:27 AM   #3
Senior Member
 
Joined: Dec 2006

Posts: 1,111
Thanks: 0

Quote:
Why can't you just use the formula for a geometric series?:
a/(1-r)
(-6)/(1-(-2))=-2
Yes, but that's the sum of an infinite quantity of terms, and in this case, the sum doesn't equal
-2 if r=-2, because if r>=1, a geometric series diverges to infinity, and the a/(1-r) formula doesn't work. You have to prove that the series converges first before you can find out what it converges to. In this case, the series would diverge by the nth term divergence test, since the lim n->00 of (-6)(-2)^n =00 .
Infinity is offline  
December 16th, 2006, 07:44 AM   #4
Newbie
 
Joined: Dec 2006

Posts: 28
Thanks: 0

Thank guys very much.. just asking from with lesson is that. i mean what kind of problem is this
Sean is offline  
January 29th, 2007, 02:13 AM   #5
Global Moderator
 
Joined: Dec 2006

Posts: 20,934
Thanks: 2208

(-6 + 12) + (-24 + 48) + (-96 + 192) + (-384 + 768) + (-1536 + 3072)

= 6 + 24 + 96 + 384 + 1536

= 2046

Sum of n terms = a(1 - r^n)/(1-r)

= -6(1 - (-2)^n)/(1 - (-2)) (for the series in the above problem)

= -2(1 - (-2)^n)

= -(-2)^(n+1) - 2

= 2^(n+1) - 2 if n is even; - 2^(n+1) - 2 if n is odd.
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
geometric, term



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
geometric series; find nth term bongantedd Algebra 2 February 26th, 2014 04:38 PM
the 12 term of a G.P kingkos Algebra 2 December 21st, 2012 07:19 PM
Sum to nth term rnck Applied Math 3 August 23rd, 2012 07:17 PM
Term by term differentiation forcesofodin Real Analysis 4 August 14th, 2010 05:50 PM
Sum to nth term rnck Real Analysis 3 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.