Answer:
32.59
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio )
4[tex](\frac{8}{9}) ^{n-1}[/tex] ← is the n th term expression
with a = 4 and r = [tex]\frac{8}{9}[/tex]
The sum of n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a(1-r^n)}{1-r}[/tex], thus
[tex]S_{20}[/tex] = [tex]\frac{4((1-\frac{8}{9}) ^{20}) }{1-\frac{8}{9} }[/tex]
= [tex]\frac{4(1-\frac{8^{20} }{9^{20} } )}{\frac{1}{9} }[/tex]
= 36( 1 - 0.0948)
= 36(0.905)
= 32.59 ( to the nearest hundredth )
