we're not going to look working at the nth term for fractional sequences so here we've got a sequence a half three sevenths five twelfths seven seven times and so on and the sequence goes on and we've been asked to work out the nth term for this through the nth term to work at the m term for fractional sequence what you need to do is consider the top line and the bottom line separately the numerators and the denominators separately so let's look at the numerators to start off with the numerators are 1 3 5 7 and the denominators are 2 7 12 and 17. so let's look at the numerators to begin with okay the numerators went one three five seven so here's the um numerators and what we're gonna do is we're gonna work the m term out for this if you need to see how to do the m term for linear sequences watch the video and term for linear sequences you should be able to know how to do this so the sequence is getting bigger by two each time so you write down the two times table so the multiples of two beneath the sequence so two four six eight and that's two n the two times tables to get from two to one four to three six to five and eight to seven you subtract one each time so the top line the numerators have an nth term of two n minus one now let's look at the denominators the denominators went 2 7 12 17. well it's getting bigger by 5 each time so you write the multiples of 5 beneath the sequence and 5n to get from 5 to 2 10 to 7 15 to 12 and 20 to 17 you subtract three so the f term for the denominators is five n subtract three so we've got the f term for the numerators and the f term for the denominators what we've got to now write as a fraction so it's going to be 2 n minus 1 over 5 n subtract minus 5 and subtract 3. so that's the nth term for this fractional sequence let's just say we wanted to work at the hundredth term in the sequence well if we wanted to know the hundredth term um the hundredth term 100 term well we've got two times 100 200 take away one which would be 199 over 5 times 100 500 take away 3 it would be 497 so the 100th term in the sequence is 199 over 497 so that's how to find the m term for fractional sequences you consider the top line and the bottom line separately and then you can then work out the nth term and put it together as a fraction and use that to work out any term missing that you want to work out