Question

Write the recursive formula for the geometric sequence.

a1 = -2 a2 = 8 a3 = -32

Answer 1

\[a_1=-2,a_2=-4a_1=-4a_2\therefore a_{n+1}=-4a_n\]

Answer 2

thats not my choices

Answer 3

What are your choices?

Answer 4

\[\sqrt{-2*8}=\sqrt{-16}=4i\] That seems to be the ratio?

Answer 5

A. an = -4 + an-1

B. an = -2 + an-1

C. an = -2 • an-1

D. an = -4 • an-1

Answer 6

when you write down a recursion, you can say
a(n+1)= -4 a(n)

or
a(n)= -4 a(n-1)

both mean the same thing:
the next a term is -4 times the current a term.
or the current a term is -4 times the previous a term
so badrefs answer is correct.

Answer 7

I don't think a recursion formula is dependent on the first term, is it? We can write the general formula \(a_n=-2{\left(-4\right)}^n\).

Answer 8

Thanks phi for straighten that out. I thought the a1,a2 were the label for the sequence members, didn't even realize it was part of the sequence terms.

Answer 9

Write the explicit formula for the geometric sequence.

a1 = -5 a2 = 20 a3 = -80

Answer 10

@badreferences if you believe wikipedia
http://openstudy.com/study#/updates/4f687d3ee4b0f81dfbb562ac
In mathematics, a recurrence relation is an equation that recursively defines a sequence, once one or more initial terms are given: each further term of the sequence is defined as a function of the preceding terms.

Answer 11

Write the explicit formula for the geometric sequence.
a1 = -5 a2 = 20 a3 = -80

Here they want the closed form: a(n)= -5*(-4)^(n-1)

Answer 12

No, the recurrence relation doesn't necessarily have to include the previous term according to Wikipedia http://en.wikipedia.org/wiki/Logistic_map . I think it's fair to say all the solutions have been provided, then.

Answer 13

In this problem, they are making a distinction between a recurrence and a closed form.