Why not? All that is really required is knowing 1/(1-x) = 1+x+x^2+... and a bit of algebraic manipulation.
There is a whole lot of background stuff here that elementary school students do not have. Way more than what you’ve stated.
a = x^1 + x^4 + x^7 + ... = x(1 + x^3 + x^6 + ...) = x/(1-x^3)
a + a^3 + a^5 + ... = a(1 + a^2 + a^4 + ...) = a/(1-a^2)
Substitute + simplify. I don't think this is beyond a (fairly smart) elementary school student.