Question

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).

Answer 1

Answer:

a₆ ≈ 25.284

Step-by-step explanation:

There is a common ratio between consecutive terms , that is

8 ÷ 6 = $\frac{32}{3}$ ÷ 8 = $\frac{4}{3}$

This indicates the sequence is geometric with nth term

$a_{n}$ = a₁ $r^{n-1}$

where a₁ is the first term and r the common ratio

Here a₁ = 6 and r = $\frac{4}{3}$ , then

a₆ = 6 × $(\frac{4}{3}) ^{5}$ = 6 × $\frac{1024}{243}$ = $\frac{6(1024)}{243}$ ≈ 25.284 ( to the nearest thousandth )

Answer 2

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