Answer:
184.08
Step-by-step explanation:
[tex]u_{1},u_{2},u_{3}.....u_{n}[/tex] form a sequence exhibiting the following property :
[tex]u_{1}=56;u_{n}=0.7u_{n-1}[/tex]
On rewriting, [tex]\dfrac{u_{n}}{u_{n-1}}=0.7[/tex] ⇒ Ratio of consecutive terms is a constant. Hence, the sequence is a Geometric Progression.
The ratio [tex]0.7[/tex] is the common ratio [tex]r[/tex]. First term = [tex]a=[/tex][tex]u_{1}=56[/tex].
Sum of [tex]n[/tex] terms of a Geometric progression is given by
[tex]S_{n}=a\times\dfrac{1-r^{n}}{1-r}[/tex] when [tex]r<1[/tex].
[tex]S_{12}=56\times(\dfrac{1-(0.7)^{12}}{1-0.7})=56\times\dfrac{0.986}{0.3}=184.083[/tex]
∴ [tex]S_{12}[/tex] to the nearest hundreth is 184.08
