1 A geometric progression \(\mathrm { u } _ { 1 } , \mathrm { u } _ { 2 } , \mathrm { u } _ { 3 } , \ldots\) is defined by
$$u _ { 1 } = 15 \quad \text { and } \quad u _ { n + 1 } = 0.8 u _ { n } \text { for } n \geqslant 1 .$$
- Write down the values of \(u _ { 2 } , u _ { 3 }\) and \(u _ { 4 }\).
- Find \(\sum _ { n = 1 } ^ { 20 } u _ { n }\).