Can anyone tell me if this is correct for this relation:
6.1 In the following sequences determine s5 if s0, s1, ... sn, ... is a sequence satisfying the given recurrence relation and initial condition.
b. sn = -sn-1 - n2 for n >= 1, s0 = 2
Can anyone tell me if this is correct for this relation:
6.1 In the following sequences determine s5 if s0, s1, ... sn, ... is a sequence satisfying the given recurrence relation and initial condition.
b. sn = -sn-1 - n2 for n >= 1, s0 = 2
Hello, papa_chango123!
What is $\displaystyle n2$?
Is that your way of writing $\displaystyle n^2$ ?
6.1) In the following sequences determine $\displaystyle s_5$
if $\displaystyle s_n$ is a sequence satisfying the given recurrence relation and initial condition.
$\displaystyle b)\;s_n \:= \:-s_{n-1}- n^2$ . for $\displaystyle n \geq 1,\;s_o = 2$
Am I reading it correctly?
It says: .$\displaystyle \underbrace{s_n}_{\text{the nth term}} \;\underbrace{=}_{\text{is}}\;\underbrace{-s_{n-1}}_{\text{neg.of preceding term}} - \underbrace{n^2}_{\text{minus n-squared}}$
So $\displaystyle s_1$ is the negative of $\displaystyle s_o$, minus $\displaystyle 1^2.$
. . $\displaystyle s_1\:=\:-2 - 1^2\:=\:-3$
And $\displaystyle s_2$ is the negative of $\displaystyle s_1$, minus $\displaystyle 2^2.$
. . $\displaystyle s_2\:=\:-(-3) - 2^2 \:=\:-1$
Then $\displaystyle s_3$ is the negative of $\displaystyle s_2$, minus $\displaystyle 3^2.$
. . $\displaystyle s_3\:=\:-(-1) - 3^2 \:=\:-8$
Hence $\displaystyle s_4$ is the negative of $\displaystyle s_3$. minus $\displaystyle 4^2.$
. . $\displaystyle s_4\:=\:-(-8) - 4^2\:=\:-8$
Therefore: $\displaystyle s_5$ is the negative of $\displaystyle s_4$, minus $\displaystyle 5^2.$
. . $\displaystyle s_5\:=\:-(-8) - 5^2\:=\:\boxed{-17}$