Ask question

Ask question

All categories

chubhunter [2.5K]

2 years ago

11

What is a formula for the nth term of a given sequence

2 answers:

Sedbober [7]2 years ago

7 0

Answer:

$a_{n} = -12-4(n-1)$

Step-by-step explanation:

We have given a arithmetic sequence.

-12,-16,-20,...

We have to find formula for a given sequence.

The general formula for nth term of sequence is :

$a_{n} = a_{1}+d(n-1)$

In given sequence,

$a_{1} = -12$

d is the common difference between consecutive terms.

d = -16-(-12) = -16+12

d = -4

Putting given values in formula, we have

$a_{n} = -12-4(n-1)$ which is the answer.

IceJOKER [234]2 years ago

5 0

Answer:

$a_n=-12-4(n-1)$

Step-by-step explanation:

The given sequence is

-12,-16,-20...

The first term of this sequence is $a_1=-12$ .

The common difference is

$d=-16--12$

$d=-16+12=-4$

The nth term of this arithmetic sequence is;

$a_n=a_1+d(n-1)$

We substitute the values for the first term and the common difference to obtain;

$a_n=-12-4(n-1)$

You might be interested in

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 29 ft/s. Its height

Ilia_Sergeevich [38]

Answer:

$\overline{v}_{@\Delta t=0.01s}=-15.22ft/s, \overline{v}_{@\Delta t=0.005s}=-15.11ft/s, \overline{v}_{@\Delta t=0.002s}=-15.044ft/s, \overline{v}_{@\Delta t=0.001s}=-15.022ft/s$

Step-by-step explanation:

Now, in order to solve this problem, we need to use the average velocity formula:

$\overline{v}=\frac{y_{f}-y_{0}}{t_{f}-t_{0}}$

From this point on, you have two possibilities, either you find each individual $y_{f}, y_{0}, t_{f}, t_{0}$ and input them into the formula, or you find a formula you can use to directly input the change of times. I'll take the second approach.

We know that:

$t_{f}-t_{0}=\Delta t$

and we also know that:

$t_{f}=t_{0}+\Delta t$

in order to find the final position, we can substitute this final time into the function, so we get:

$y_{f}=29(t_{0}+\Delta t)-22(t_{0}+\Delta t)^{2}$

so we can rewrite our formula as:

$\overline{v}=\frac{29(t_{0}+\Delta t)-22(t_{0}+\Delta t)^{2}-y_{0}}{\Delta t}$

$y_{0}$ will always be the same, so we can start by calculating that, we take the provided function ans evaluate it for t=1s, so we get:

$y_{0}=29t-22t^{2}$

$y_{0}=29(1)-22(1)^{2}$

$y_{0}=7ft$

we can substitute it into our average velocity equation:

$\overline{v}=\frac{29(t_{0}+\Delta t)-22(t_{0}+\Delta t)^{2}-7}{\Delta t}$

and we also know that the initil time will always be 1, so we can substitute it as well.

$\overline{v}=\frac{29(1+\Delta t)-22(1+\Delta t)^{2}-7}{\Delta t}$

so we can now simplify our formula by expanding the numerator:

$\overline{v}=\frac{29+29\Delta t-22(1+2\Delta t+\Delta t^{2})-7}{\Delta t}$

$\overline{v}=\frac{29+29\Delta t-22-44\Delta t-22\Delta t^{2}-7}{\Delta t}$

we can now simplify this to:

$\overline{v}=\frac{-15\Delta t-22\Delta t^{2}}{\Delta t}$

Now we can factor Δt to get:

$\overline{v}=\frac{\Delta t(-15-22\Delta t)}{\Delta t}$

and simplify

$\overline{v}=-15-22\Delta t$

Which is the equation that will represent the average speed of the ball. So now we can substitute each period into our equation so we get:

$\overline{v}_{@\Delta t=0.01s}=-15-22(0.01)=-15.22ft/s$

$\overline{v}_{@\Delta t=0.005s}=-15-22(0.005)=-15.11ft/s$

$\overline{v}_{@\Delta t=0.002s}=-15-22(0.002)=-15.044ft/s$

$\overline{v}_{@\Delta t=0.001s}=-15-22(0.001)=-15.022ft/s$

5 0

3 years ago

What equation is used to find the vertex form of a parabola with the vertex (h, k)?

makkiz [27]

Answer:

y=a $(x-h)^{2}$ +h

Step-by-step explanation:

equation for vertex form of a parabola is,

y=a $(x-h)^{2}$ +h

8 0

2 years ago

Read 2 more answers

A plant has a height of 8 1/4 inches what is the height of the plant after it grows 1 7/8 inches?

zaharov [31]

10 1/8 inches. .............................

8 0

3 years ago

Read 2 more answers

Which statement is true about an angle?

Sveta_85 [38]

Where are the statements please?

4 0

2 years ago

Read 2 more answers

Solve the literal equation for y.<br> 4x - 2y = 10

MA_775_DIABLO [31]

Answer:

it could be that x is 4 and y 3

Step-by-step explanation:

3 0

2 years ago