Question

Write an explicit rule for the nth term of the geometric sequence. NO LINKS!!!!​

Answer 1

Answer:

$7 \\ 5 \times {1.1}^{x - 1} \\8 \\ \frac{1}{9} = a \times {( - 3)}^{8 - 1} \\ a = \frac{1}{9} \times \frac{ - 1}{ {3}^{7} } = \frac{ - 1}{ {3}^{9} } \\ \\ \frac{ - 1}{ {3}^{9} } \times {( - 3)}^{x - 1}$

Answer 2

Answer:

see explanation

Step-by-step explanation:

The nth term ( explicit rule ) of a geometric sequence is

$a_{n}$ = a₁ $(r)^{n-1}$

where a₁ is the first term and r the common ratio

(7)

$a_{n}$ = 5 $(1.1)^{n-1}$

(8)

Given a₈ = $\frac{1}{9}$ , then

a₁ $(-3)^{7}$ = $\frac{1}{9}$

a₁ × - 2187 = $\frac{1}{9}$ ( divide both sides by - 2187 )

a₁ = - $\frac{1}{19683}$

Then

$a_{n}$ = - $\frac{1}{19683}$ $(-3)^{n-1}$