All categories

3 years ago

The nth term of a sequence is 8(n+3) what are the first four terms?

Mathematics

1 answer:

8090 [49]3 years ago

4 0

Answer:

32, 40, 48, 56

Step-by-step explanation:

$a_n= 8(n+3)...(given) \\\\ a_1= 8(1+3) = 8 \times 4 = 32 \\ \\ \: a_2= 8(2+3) = 8 \times 5 = 40 \\ \\ a_3= 8(3+3) = 8 \times 6 = 48 \\ \\ a_4= 8(4+3) = 8 \times 7 = 56 \\$

You might be interested in

A fair coin is tossed repeatedly with results Y0, Y1, Y2, . . . that are 0 or 1 with probability 1/2 each. For n ≥ 1 let Xn = Yn

Gekata [30.6K]

Answer:

False. See te explanation an counter example below.

Step-by-step explanation:

For this case we need to find:

$P(X_{n+1} = | X_n =i, X_{n-1}=i') =P(X_{n+1}=j |X_n =i)$ for all $i,i',j$ and for $X_n$ in the Markov Chain assumed. If we proof this then we have a Markov Chain

For example if we assume that $j=2, i=1, i'=0$ then we have this:

$P(X_{n+1} = | X_n =i, X_{n-1}=i') =\frac{1}{2}$

Because we can only have $j=2, i=1, i'=0$ if we have this:

$Y_{n+1}=1 , Y_n= 1, Y_{n-1}=0, Y_{n-2}=0$ , from definition given $X_n = Y_n + Y_{n-1}$

With $i=1, i'=0$ we have that $Y_n =1 , Y_{n-1}=0, Y_{n-2}=0$

So based on these conditions $Y_{n+1}$ would be 1 with probability 1/2 from the definition.

If we find a counter example when the probability is not satisfied we can proof that we don't have a Markov Chain.

Let's assume that $j=2, i=1, i'=2$ for this case in order to satisfy the definition then $Y_n =0, Y_{n-1}=1, Y_{n-2}=1$

But on this case that means $X_{n+1}\neq 2$ and on this case the probability $P(X_{n+1}=j| X_n =i, X_{n-1}=i')= 0$ , so we have a counter example and we have that:

$P(X_{n+1} =j| X_n =i, X_{n-1}=i') \neq P(X_{n+1} =j | X_n =i)$ for all $i,i', j$ so then we can conclude that we don't have a Markov chain for this case.

6 0

3 years ago

1. Johnny typically drives his truck between 250 and 300 miles a day for work. Last week he worked 5 days and drove a total of 1

Schach [20]

Hey I’m in class but it is fine to help a friend so that answer is 1350

5 0

3 years ago

Read 2 more answers

Pennsylvania has a land mass of 44,816 square miles.What is the land area of Pennsylvania rounded to the nearest hundred?

sineoko [7]

The answer would be 44,800 if you want to round the hundreds place

4 0

3 years ago

У - (-3y)<br><br> Iam confused on how to do this

jeyben [28]

Answer:

The answer is 4y.

Step-by-step explanation:

First you would solve the parentheses, which would be -1(-3y) which would equal positive 3y, and y+3y=4y. I apologize if I misunderstood the problem ^^

8 0

3 years ago

Kelly earns $178.50 in interest on an account that earns simple interest at a rate of 4%. If she kept the money in the account f

Otrada [13]

Answer:

$892.50

Step-by-step explanation:

The amount of interest earned is given by ...

I = Prt

Filling in the given values, we have ...

$178.50 = P·0.04·5

Dividing by 0.20 gives ...

$178.50/0.20 = P = $892.50

The principal amount in Kelly's account is $892.50.

7 0

3 years ago