Question

how can i do this?
The following function defines a recursive sequence.

f(0) = -3

f(1) = 6

f(n ) = -2•f(n -1) - f(n - 2); for n > 1

Which of the following sequences is defined by this recursive function?

a. -3, 6, -9, -12, …
b. -3, 20, -95, 480, …
c. -3, 6, -9, 12, …
d. -3, -20, -95, -480, …

Answer 1

n=2?

Answer 2

have you done geometric sequences?

Answer 3

not much..

Answer 4

lemme rewrite that in a bit different notation\(\huge{ a_o = -3\qquad \qquad a_1=6\\ \quad \\
a_n = -2\cdot a_{n-1}-a_{n-2}}\)

Answer 5

if you want to find the \(\bf n^{th}\) term, you plug that as your "n", so to match against your choices, you got the 1st one and the 2nd one, get the 3rd, n = 2, and the 4th one, n = 3

Answer 6

so u would juss add one to each nth term?

Answer 7

a2=-a3??

Answer 8

hmm well... \(\bf \Large {a_o = -3\qquad \qquad a_1=6\\ \quad \\
a_n = -2\cdot a_{n-1}-a_{n-2}\\ \quad \\ \quad \\
a_2 = -2\cdot a_{2-1}-a_{2-2}\\ \quad \\
a_3 = -2\cdot a_{3-1}-a_{3-2}}\)

Answer 9

i need to find wat a2 and a3 is?

Answer 10

yes, once you find what \(\bf a_2\) is, you can go and find \(\bf a_3\)

\(\large\bf a_2 = -2\cdot a_{2-1}-a_{2-2}\implies a_2=-2\cdot a_1-a_0\)

Answer 11

we know what \(\bf a_1 \ and \ a_0\) are, so we can just plug them in, to get \(\bf a_2\)

Answer 12

a2=-2x6-3 ?

Answer 13

\(\large\bf {a_2 = -2\cdot a_{2-1}-a_{2-2}\implies a_2=-2\cdot a_1-a_0\\ \quad \\
a_2 = -2\cdot (6)-(-3)}\)

Answer 14

a2=-9

Answer 15

yeap

Answer 16

i understand it now o-o. thanks so much : ))!!!!

Answer 17

\(\large \bf {a_3 = -2\cdot a_{3-1}-a_{3-2}\implies a_3=-2\cdot a_2-a_1}\)

Answer 18

yw

Answer 19

a3=18-6
a3=12 !:D

Answer 20

:)