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Answer:
a₆ ≈ 25.284
Step-by-step explanation:
There is a common ratio between consecutive terms , that is
8 ÷ 6 = [tex]\frac{32}{3}[/tex] ÷ 8 = [tex]\frac{4}{3}[/tex]
This indicates the sequence is geometric with nth term
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 6 and r = [tex]\frac{4}{3}[/tex] , then
a₆ = 6 × [tex](\frac{4}{3}) ^{5}[/tex] = 6 × [tex]\frac{1024}{243}[/tex] = [tex]\frac{6(1024)}{243}[/tex] ≈ 25.284 ( to the nearest thousandth )
Step-by-step explanation:
it is a geometric sequence.
the common ratio or factor is 4/3.
I got this by simply trying to get from the 2nd to the 3rd term.
8×x = 32/3
24x = 32
x = 32/24 = 16/12 = 8/6 = 4/3
s1 = 6
s2 = s1 × 4/3 = 6 × 4/3 = 24/3 = 8
s3 = s2 × 4/3 = s1 × 4/3 × 4/3 = 6 × 16/9 = 2 × 16/3 = 32/3
sn = s1 × (4/3)^(n-1)
s6 = 6 × (4/3)⁵ = 6 × 1024/243 = 2 × 1024/81 = 2048/81 =
= 25.284