# How do you find the explicit formula for the following sequence 3, 7, 11, 15,...?

The general formula is ${a}_{n} = 4 n - 1$ for $n = 1 , 2 , 3 , \ldots$
It is an arithemtic progession with first term ${a}_{1} = 3$ and ratio $r = 4$
${a}_{n} = {a}_{1} + \left(n - 1\right) \cdot r \implies {a}_{n} = 3 + \left(n - 1\right) \cdot 4 = 4 \cdot n - 1$