Fraction Sequences

[Signora Castafiore]

My daughter is stuck on her homework and I can't help!

Find the next two terms of these fraction sequences:


3, 2/3 , 2, 4/3 , 8/3 , _, _,


3/4 ,4/5 , 3/5 , 12/25, _ ,_ ,


Any help would be appreciated.

[Guest]

Hi

I think this is a problem for TinTin and Captain Haddock.

I can't complete the sequences, could you please re-check the questions and If there are any errors re-send them?

[maybe]

second one - a possible solution is

3/4 x 4/5 (first and second in the series)=3/5 i.e the next in the series

4/5 x 3/5 (second and third in series) =12/25 (4th is series)

therefore

Next in series is

3/5 x 12/25 (third and 4th in series)= 36/125

Is this one of the answers given? It doesn't seem very conclusive to me, since the pattern does not explain how to get from 3/4 to 4/5 (1st to 2nd in series)

But maybe this is what they intend.

[sj355]

Find the next two terms of these fraction sequences:


3, 2/3 , 2, 4/3 , 8/3 , _, _,

Multiplyng the two preceding numbers gives the next:


3 x 2/3= 6/3=2
2/3 x 2 = 4/3
2 x 4/3=8/3
4/3 x 8/3 =32/9
8/3 x 32/9=256/27


3/4 ,4/5 , 3/5 , 12/25, _ ,_ ,

this is given by mulitplying the numerator of the two preciding numbers and also the denominators of the preceding two:

hence 3/4 x 4/5 = 12/20=3/5
4/5 x 3/5 =12/25
3/5x12/25=36/125
12/25x36/125=432/3125


These are horrible numbers that lack elegance! Where did you find them?