You've given us a single term of an arithmetic series. So far, there are an infinite number of different series that it could be a member of. ... In fact, ANY function f (n) for which f (7) = 54 produces a suitable series for whole-number values of 'n'. Here are a few: ... T(n) = n + 47. ... T (n) = 8n - 2. ... T (n) = -10n + 124 .