Sequences advice please- tips on solving nth terms?

Hi all

We've just started a sequences topic, and Ive never been good at sequences (finding the nth term) at GCSE and now Im struggling to find the nth terms again.

Once Im given the rule its easy, its just finding it

Does anyone have any tips on the best ways to improve myself at finding the nth terms? We have also now started Sigma notation (using r) so any ideas how to help me?

I would appreciate all help, as I really need to brush up my skills, but my text book is utter rubbish at providing advice

Also, I can do simple ones, e.g. 5,9,13,17...

Its ones that involve fractions and negatives for example:

2/3 + 5/9 + 8/27 + 11/81 + 14/243 + 17/729

and

1 x 4 - 3 x 7 + 5 x 10.......+ 29 x46

Help?

Thanks for any advice given!