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MathPhys

Answer:

an = 10 (-8)^(n-1)

Step-by-step explanation:

In a geometric series, each term is multiplied by a common ratio to get the next term.  Such that:

an = a₁ (r)^(n-1)

Here, the first term, a₁, is 10.  The common ratio, r, is -8, because each term is multiplied by -8 to get the next term.  So:

an = 10 (-8)^(n-1)

Your answer is correct, well done!

MrRoyal

The recursive rule of the geometric sequence is [tex]a_{n+1}= -8a_n[/tex] where a1 = 10

How to determine the recursive rule?

The geometric sequence is given as:

10, −80,  640, −5120, ...

Start by calculating the common ratio (r)

[tex]r = \frac{a_{n-1}}{a_n}[/tex]

Substitute 2 for n

[tex]r = \frac{a_{2}}{a_1}[/tex]

Substitute known values

[tex]r = \frac{-80}{10}[/tex]

Evaluate the quotient

[tex]r = -8[/tex]

Substitute -8 for r in [tex]r = \frac{a_{n+1}}{a_n}[/tex]

[tex]-8 = \frac{a_{n+1}}{a_n}[/tex]

Cross multiply

[tex]a_{n+1}= -8a_n[/tex]

Hence, the recursive rule of the geometric sequence is [tex]a_{n+1}= -8a_n[/tex] where a1 = 10

Read more about geometric sequence at:

brainly.com/question/24643676

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