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2 years ago

Find the value of x and y given that p//q. Type answers alphabetically, and separate by a comma and a space

Mathematics

1 answer:

butalik [34]2 years ago

8 0

Answer:

Step-by-step explanation:

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If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.

Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have $S_1=3\times2^{1-1}+2(-1)^1=3-2=1$ , which agrees with the initial value S₁ = 1.

• Assume the closed form is correct for all n up to n = k. In particular, we assume

$S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}$

and

$S_k=3\times2^{k-1}+2(-1)^k$

We want to then use this assumption to show the closed form is correct for n = k + 1, or

$S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}$

From the given recurrence, we know

$S_{k+1}=S_k+2S_{k-1}$

so that

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)$

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}$

$S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)$

$S_{k+1}=3\times2^k-2(-1)^k$

$S_{k+1}=3\times2^k+2(-1)(-1)^k$

$\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}$

which is what we needed. QED

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2 years ago

The Briarwood Middle School chess club has 55 members. 22 of the members are in seventh grade. What percent of the members of th

Jet001 [13]

Answer:

40%

Step-by-step explanation:

22/55 = ?/100

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2 years ago

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PLEASE HELP ME!John invests $2,975 at 4% interest compounded annually. What will be the balance in the account after 2.5 years?

ch4aika [34]

2975(1+0.04)^2.5=???? Hope it helps :-)

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2 years ago

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If you flip a coin 150 times about how many times would you expect to get heads

meriva

A coin has two sides, which means it has a 1/2 chance of landing on each individual side when you flip the coin. Since there is a 1/2 chance of landing on each side, you could expect the coin to land on "Heads' 75 times.

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svetlana [45]

The student went wrong in step three. the solutions should have been -3 and 5

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