Tips for solving nth term questions (Maths)

I have troubles trying to find the express in terms of n for a patterns, are there any methods or tips to solve them?

For example - 1,3,7,15,31...

this one is a_1 = - 1 and a_n = - 1 + 2^n , n ≥ 2....you just have to play with the terms given

note that if the next term { not given } = 54 then mine won't work either....

most times a sequence will not have a ' nice ' algorithm for its terms

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