Question

Determine the next number in the sequence: a) 1/4. 4/9. 3/5. 8/11. 5/6. 1/32.

b) How is the relation of the sequence in "a)" different from: 1. 4. 11. 29. 76. 199.

Answer 1

The sequence given is not correct if the following logic goes correctly with this. Here what can be argued,

4/9 - 1/4 = 7/36

3/5 - 4/9 = 7/45 ( 45 = 36 + 9 )

8/11 - 3/5 = 7/55 (55 = 45 + 10)

5/6 - 8/11 = 7/66 (66 = 55 + 11)

now if there is 12/13 in stead of 1/32 we get,

12/13 - 5/6 = 7/78 (78 = 66 + 12 )

Then, the next number will be,

12/13 + 7/(78+13) = 12/13 + 7/91( = 1/13 ) = 12/13 + 1/13 = 1.

So the next number is 1.

The next sequence is

1,        4,        11,      29,        76,        199

(-)= 3,         7,         18,       47,        123

(-)=        4          11         29         76.

So we can write,

=>

=> .

The difference is that in the first one the denominators are getting added by sequentially starting from 9 and numerator stays fixed at 7.

In the latter case, the logic is just described above. difference is hopefully clear from these two.