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Yogi
Posts:
323
Registered:
12/6/04


Re: sequences ahhhhhh!!!!! help
Posted:
Sep 10, 2004 11:18 AM


On 10 Sep 04 10:42:44 0400 (EDT), sam stewart wrote: >4 8 16 32 > +  +  +  >1 5 25 125 > >find ths sum to infinite > >I have the formula to work out the sum to infinite but i cant work out >what the common difference of the terms are. > >Sn to infinite = a1/(1r) >(for infinite sequences when 1<r<1) > >sn= sum of the first n numbers >a1 is the first number in the sequence >r= the common ratio of the sequence > >i am sure this is the correct formulae? but what is the common >difference if you can help me i would be very grateful as i am >struggling although it may be a very simple question?????? > >sam
This is, as you suspect, a geometric series but the way it is written may be misleading you! Notice that it starts at with "4" rather than 1: 4+ 8/5+ 16/25+ ...
If you take a 4 out of each term: 4(1)+ 4(2/5)+ 4(4/25)+ ... See what happens? This is simply 4(2/5)^0+ 4(2/5)+ 4(2/5)^2+ ..., a geometric series with common ration (NOT common "difference") 2/5.
In any geometric series you can find the common ratio by dividing a term by the preceding term: 8/5 divided by 4 = 2/5 16/25 divided by 8/5= 2/5, 34/125 divided by 16/25= 2/5.
So: a1= 4 and r= 2/5 (which IS between 1 and 1).
Can you find the sum now?



