In a question like:

(2t − 3) + (3t + 1) + (5t + 2) +…


(t − 5) + 3t + (3t + 1) +…

I find myself just using trial and error to find the pronumeral that gives a common difference. I feel like that is very time consuming and could possibly be solved with a formula (if there is one).

I know of formulas that find the nth term such as:

Tn = Tn-1 + d


Tn = a + (n-1)d

I either don't know how to relate these formulas to the questions above or they are not related. Is trial and error the only method here? thanks.



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