Pick some number [tex]a[/tex]. Then multiply this by another number [tex]r[/tex]. Keep doing this and you generate a geometric sequence [tex]a,ar,ar^2,ar^3,\ldots[/tex].
The 11th and 12th terms in this sequence are then [tex]ar^{10}[/tex] and [tex]ar^{11}[/tex] (because you get the 11th term after you multiply by [tex]r[/tex] 10 times, and the 12th term after 11 times).
The first term is, of course, [tex]a[/tex]. We're given [tex]a=4[/tex] and [tex]r=\frac12[/tex]. The sum of the 11th and 12th terms are then computed as shown in your picture.
