Some arithmetic means are inserted between 3 and 51…

Step 1. The means. The $3$rd mean is $3 + 3d$, and the last is $3 + md = 51 - d$.

Step 2. The ratio. $4(3 + 3d) = 51 - d$, so $13d = 39$ and $d = 3$.

Step 3. How many. $d = \dfrac{48}{m + 1} = 3$, so $m + 1 = 16$ and $m = 15$.