Question

Write the next term of the sequence:
1/2, 4/3, 9/7, 49/16, ...

Answer 1

try figuring out what is the difference between 49/16 and 9/7, then 9/7 with 4/3, then 4/3 and 1/2

Answer 2

This is complicated, but I have reason to believe that the answer is 256/32 = 8.

Answer 3

Look, after 1/2, the numerators are the squares of the PREVIOUS denominator.
That's how I got 256.

And the denominators after 1/2, are always the previous denominator plus a perfect square... like this :
3 = 2 + 1
7 = 3 + 4
16 = 7 + 9

So I figured the next denominator must be the previous denominator, 16, plus the next perfect square, which also happened to be 16, so..

32 = 16 + 16

Answer 4

saw that

Answer 5

so the next demoninator should be 49+16

Answer 6

but I don't see any holonomic sequence

Answer 7

me too I do not see a sequence... I am having a hard time solving this.

Answer 8

I see the denominator but not the numerator

Answer 9

I get it now

Answer 10

the numerator is the square of the denominator

Answer 11

next is 256/65

Answer 12

saw it! thanks!

Answer 13

@panlac01
Why is the next denominator 65?

Answer 14

the denominator is the sum of the numerator and denominator of the previous fraction except 1/2

Answer 15

49+16

Answer 16

Makes sense... Far simpler

Answer 17

lol

Answer 18

I tried my best to make sense of it.. it looks like I'm complicating things too much. Thanks!

Answer 19

thanks guys!

Answer 20

np. no textbook can teach you this, so I answered to my fullest.

Answer 21

haha!

Answer 22

I wasn't expecting to learn this through textbooks... this is intuition :D

Answer 23

:)