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3 years ago

SAVING/INVESTING

1 answer:

4 0

I don’t know the answer to this but I have an app called Socratic, it helps out with problems like this, download it and take a picture of what you are looking for, and it will give you the answers. I hope this helps..

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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

6 0

3 years ago

Help me out, please.

Assoli18 [71]

Y+4=2/3(x+3)

(-3,-4)(3,0)
1.find the slope
m=y2-y1/x2-x1
m=0-(-4)/3-(-3)
m=4/6
m=2/3

y-(-4)=2/3(x-(-3))
y+4=2/3(x+3) point-slope form

4 0

3 years ago

(2×4)×7=2×(7×4) what property does this demonstrate

notka56 [123]

Well,

As we can see, the only difference is that the parentheses have moved.

This is an example of the associative property. It is specifically of multiplication, because products are used in this case.

Just as a test, let's see whether they are really equal.

Following PEMDAS, we get:
(2*4)7 = 2(7*4)
(8)7 = 2(28)
56 = 56

They are equivalent.

8 0

3 years ago

Read 2 more answers

A student solved the equation 2x+6=12 using algebra tiles. incorrectly says the solution is 9. Solve the equation. What mistake

alexdok [17]

Instead of subtracting 6 from 12 then dividing they added 6 to 12 & ended up with 18. 18 by 2 is 9.

8 0

3 years ago

Q1: Write the sum of numbers as a product of their GCF and another sum. 24+16 Q2: Write the sum of numbers as a product of their

Anastaziya [24]

Answer:

for the points

Step-by-step explanation:

u dumb tbh

7 0

3 years ago