Question

I don't get this. Can someone explain it better?

Answer 1

Pick some number $a$. Then multiply this by another number $r$. Keep doing this and you generate a geometric sequence $a,ar,ar^2,ar^3,\ldots$.

The 11th and 12th terms in this sequence are then $ar^{10}$ and $ar^{11}$ (because you get the 11th term after you multiply by $r$ 10 times, and the 12th term after 11 times).

The first term is, of course, $a$. We're given $a=4$ and $r=\frac12$. The sum of the 11th and 12th terms are then computed as shown in your picture.