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.