Stewart's Sequences 5 of 5

Firstly, let's total up the three terms given.

$\begin{matrix} (x+1)& =1x+1 \\ (x+1)+(x+3) & =2x+4 \\ (x+1)+(x+3)+(x+5) & =3x+9 \end{matrix}$

Clearly we can see that we have a pattern. This pattern is: $n^2 + nx$ .

Now we're told that when $n=38$ , $n^2 + nx = 2014$ . So we have: $38^2 +38x =2014$ Firstly, we can divide by 38, to give: $38 + x = 53$ Now, subtracting 38, we can see that: $x = 15$ Now, the digital sum of 15 is: $1 + 5 = \boxed 6$