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3 years ago

The sequence {an) is defined by ao = 1 and

Mathematics

1 answer:

otez555 [7]3 years ago

6 0

<h3>Answer: 31</h3>

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Work Shown:

Use the value of a0 to find the value of a1. The idea is you double the previous value, and then add 1.

$a_{n+1} = 2*(a_n) + 1\\\\a_{0+1} = 2*(a_0) + 1\\\\a_{1} = 2*(1) + 1\\\\a_{1} = 3\\\\$

Which is then used to find the value of a2. Follow the same process as before (double the previous value and then add 1).

$a_{n+1} = 2*(a_n) + 1\\\\a_{1+1} = 2*(a_1) + 1\\\\a_{2} = 2*(3) + 1\\\\a_{2} = 7\\\\$

This is used to find a3

$a_{n+1} = 2*(a_n) + 1\\\\a_{2+1} = 2*(a_2) + 1\\\\a_{3} = 2*(7) + 1\\\\a_{3} = 15\\\\$

Finally we can now find a4

$a_{n+1} = 2*(a_n) + 1\\\\a_{3+1} = 2*(a_3) + 1\\\\a_{4} = 2*(15) + 1\\\\a_{4} = 31\\\\$

Recursive sequences like this aren't too bad if n is small, but as n gets larger, things become more tedious. For those cases, its best to try to find a closed form equation. If not, then the next best thing is using a spreadsheet to automate the process.

You might be interested in

Volume (to the nearest tenth)

Ivenika [448]

Answer:

913

Step-by-step explanation:

cylinder:

radius=5.6 height=7

first lets find the volume of the cylinder the formula for the volume of a cylinder is pi times radius squared times height. so after plugging in the height and radius you get 689.64242

cone:

radius=5.6 height=6.8

now the volume of the cone, the formula for the volume of a cone is pi times radius squared times height/3. so after plugging in the height and radius of the cone you get 223.31278

so 689.64242 + 223.31278= 912.9552 and that rounded to the nearest tenth is 913

3 0

2 years ago

On a recent trip to a local orchard, the Morgan family picked four different kinds of apples - Braeburn, Cortland, Fuji, and Rom

ivanzaharov [21]

Answer:

Morgan family picked 144 Braeburn apples, 96 Cortland apples, 72 Fuji apples and 48 Rome apples.

Step-by-step explanation:

Let B, C, F and R represent Braeburn apples, Cortland apples, Fuji apples, and Rome apples respectively.

We have been given that Morgan family picked a total of 360 apples. We can represent this information in an equation as:

$B+C+F+R=360...(1)$

We are told that Morgan family picked twice as many Braeburn as Fuji. We can represent this information in an equation as:

$B=2F...(2)$

We are told that Morgan family picked twice as many Cortland as Rome, that is:

$C=2R...(3)$

We are told that Morgan family picked 50% more Fuji than Rome, that is:

$F=1.5R...(4)$

Upon substituting equation (4) in equation (2), we will get:

$B=2(1.5)R$

$B=3R$

Now, each apple in in terms of Rome apples, so we will get:

$3R+2R+1.5R+R=360$

Let us solve for R.

$7.5R=360$

$\frac{7.5R}{7.5}=\frac{360}{7.5}$

$R=48$

Therefore, Morgan family picked 48 Rome apples.

Upon substituting $R=48$ in (3), we will get:

$C=2R\Rightarrow 2(48)=96$

Therefore, Morgan family picked 96 Cortland apples.

Upon substituting $R=48$ in (4), we will get:

$F=1.5R\Rightarrow 1.5(48)=72$

Therefore, Morgan family picked 72 Fuji apples.

Upon substituting $F=72$ in (2), we will get:

$B=2F\Rightarrow 2(72)=144$

Therefore, Morgan family picked 144 Braeburn apples.

3 0

3 years ago

The population of a particular type of bacteria is known to triple in 22 days. What is the daily growth rate

Paul [167]

Answer: ∛(3)

Step-by-step explanation:

Suppose that at day 0 the population was A.

at day 3, the population will be: 3*A

at day 6, the population will be 3*(3*A) = A*3^2

then, at day N = 3*n (where n = 0, 1, 2.....) the population will be:

P(N) = A*3^n

Particularly, if we take n = 1/3 we will have:

N = 3*1/3 = 1

This means that this is the first day after the day 0.

P(1) = A*3^(1/3)

(then in day one, the population grow by a factor of 3^(1/3))

N = 2 is when n = 2/3, then:

P(2) = A*3^(2/3)

The quotient between P(2) and P(1) is equal to the growth between day one and day two, this should be the same as the growth between day zero and day one.

A*3^(2/3)/(A*3^(1/3)) = 3^( 2/3 - 1/3) = 3^(1/3)

So we found that the daily growth rate is 3^(1/3) or ∛(3)

3 0

3 years ago

20% of the patron's order the chef's special. The probability that 2 out of the next ten customers will order the chef's special

kotegsom [21]

Answer:

$P(x =2) = 0.3020$