Question

Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1?

9.6, –4.8, 2.4, –1.2, 0.6, ...

f(n + 1) = –0.5f(n)
f(n + 1) = 0.5f(n)
f(n + 1) = f(0.5n)
f(n + 1) = f(–0.5n)

Answer 1

@jim_thompson5910

Answer 2

find f(2) using the sequence generating equations given
Like for example let's look at the first equation
f(1)=9.6
replace n with 1
f(1+1)=-0.5f(1)
what does this give f(2) as ?

Answer 3

it would be f(2)=-0.5f(1) @freckles

Answer 4

right @freckles

Answer 5

hello @freckles

Answer 6

and what does that give us for f(2)?

Answer 7

-0.5f(1) which i believe would be -0.5 right?

Answer 8

hmmm... I don't think f(1) was 1

Answer 9

I think f(1) was given as 9.6

Answer 10

ok then @freckles

Answer 11

so what is -0.5f(1)=?

Answer 12

i am not sure @freckles

Answer 13

f(1)=9.6
replace f(1) with 9.6

Answer 14

-0.5*9.6=?

Answer 15

-4.8 @freckles

Answer 16

right isn't that the next number in the sequence?

Answer 17

yup @freckles

Answer 18

the bottom two choices make no sense
the only two that make sense are the first two
and the first one makes most sense because the terms of the sequence alternate in sign
but we also notice that each term is a half of the previous term

Answer 19

yup you are right @freckles

Answer 20

could you help me on a few more @freckles

Answer 21

i actually have to be going here
sorry
but there are lots of people on and are helping

Answer 22

ok but thank you @freckles