Use dimensions to check v = u + at. The distance a body covers in its nth second is written sn = u…

Step 1. (a). $[v] = [\text{L}\,\text{T}^{-1}]$, $[u] = [\text{L}\,\text{T}^{-1}]$, $[at] = [\text{L}\,\text{T}^{-2}][\text{T}] = [\text{L}\,\text{T}^{-1}]$. All alike: the equation may be right (it is).

Step 2. (b), as written. The terms look like speeds while $s_n$ is a length, so the check seems to fail.

Step 3. The hidden second. $s_n$ is the distance in one second, so each term is really multiplied by $1\ \text{s}$: $s_n = \left[u + \frac{a}{2}(2n - 1)\right] \times (1\ \text{s})$. With that, every term is a length.