I help with STEM and have been given the following sequence of fractions. {4/5, 3/4, 16/19, 25/26, 12/11, 11/10, 24/25, 33/32, 20/17, 19/16} and asked to predict the next five fractions.
So I took the second fraction nominator and subtracted from the first fraction nominator and then incremented this process across the ten fractions given.
{-1, 13, 9, -13, -1, 13, 9, -13, -1}, so from this I find a possible pattern {-1, 13, 9, -13} for nominator. So I took the second fraction denominator and subtracted from the first fraction denominator and then incremented this process across the ten fractions given.
{-1, 15, 7, -15, -1, 15, 7, -15, -1}, so from this I find a possible pattern {-1, 15, 9, -15} for denominator. So I roll this out in a Mathematica program:
{4/5, 3/4, 16/19, 25/26, 12/11, 11/10, 24/25, 33/32, 20/17, 19/16, 32/31, 41/38, 28/23, 27/22, 40/37, 49/44, 36/29, 5/4, 48/43, 57/50, 44/35, 43/34, 8/7, 65/56}. After 50,000 iterations I get convergence to 100/133. So I thought why not try ChatGPT 4.0 and the Wolfram plugin, so I signed up to an account. This would be the kind of assistance you would hope to have to confirm answers if you have no one else to ask.
However it was too much for ChatGPT 4.0 and the Wolfram plugin.
Can someone kindly help me to say that I used the correct approach above? or if there is a more correct way to predict the sequence.