All categories

1 year ago

What is the nth term rule of the linear sequence below?

Mathematics

1 answer:

aleksklad [387]1 year ago

4 0

Answer:

$a_n=5+2n$

Step-by-step explanation:

Each term is 2 more than the previous term, so the common difference is 2.

Let $a_n$ be the nth term of the sequence. Then, the first term is $a_1=7$ .

The second term is $a_2=7+2=9$ , and the third term is $a_3=7+2+2=11$ .

Therefore, every term can be written as

$a_n=7+\underbrace{2+2\cdots +2}_{n-1~\text{times}}$ .

Since repeated addition is multiplication, this can be written as

$a_n=7+2(n-1),$

which is the nth term rule of the linear sequence.

This could also be expanded to $\boxed{a_n=5+2n.}$

You might be interested in

Find the derivative of 3e^y+x=y

Sindrei [870]

You have the following function:

$y=3e^y+x$

Derivate implictly the previous expression, as follow:

$y^{\prime}=3e^yy^{\prime}+1$

Where you have used that:

$(e^y)^{\prime}=e^yy^{\prime}$

Then, the implicit derivative of the given expression is:

$y^{\prime}=3e^yy^{\prime}+1$

Next, solve for y' as follow:

$\begin{gathered} y^{\prime}-3e^yy^{\prime}=1 \\ (1-3e^y)y^{\prime}=1 \\ y^{\prime}=\frac{1}{1-3e^y} \end{gathered}$

4 0

1 year ago

If anyone could solve this question for me while showing the steps. It would be GREATLY appreciated

Blizzard [7]

this is a very annoying problem, with lots of steps. it is on a next level of dragging on and on

Step-by-step explanation:

You can split this into different shapes. A triangle, a rectangle, and a void of a quarter circle. The total area is rectangle+triangle-quarter circle.

We find the second side of the triangle by doing 65-48=17

We then use the pythagorean theorem to find the third length. This is about 49.1426.

We can then use whatever method you'd like for finding the area of the triangle. it turns out to be about 417.7125

Next, we find the rectangle, easy enough, 49.1426*48=2358.8448

which seems a bit scuffed until you realize that the diagram itself is scuffed as well. Great, quarter circle next

16*16*pi/4=201.0619

Alright, now to combine it to find the area.

417.7125+2358.8448-201.0619=2575.4954

great, now let's find the perimeter, simple enough. Curved perimeter+straight perimeter-that one corner in the bottom right

52+48+49.1426+65-32+25.1327=207.2753

and now we convert to meters

207.2753feet=63.1775meters

We are almost done! Now let's find the cost.

Fencing first:

63.1775*8.50=537.01

Then the cement

2575.4954*5.50=14165.2247

Then we add it up and apply tax:

537.01+14165.2247=14702.2347

14702.23*1.13=$<u><em>16613.53</em></u>

if you find anything wrong message me, I may have made errors because its 10pm and i need sleep. I recommend you work through my steps on your own as well. There might be complications with rounding as well, so yea. Hope this helps!

3 0

2 years ago

A toy baseball bat comes with 3 plastic balls. The balls are in a box that is a rectangular solid. The box is just big enough to

vodomira [7]

Answer:

31.4 in³

Step-by-step explanation:

The box is just big enough to hold the 3 balls, so it must have a length 6 times the radius of each ball, a width 2 times the radius, and a height 2 times the radius.

The volume of the box is:

V = (6r)(2r)(2r)

V = 24r³

The volume of the 3 balls is:

V = 3 (4/3 π r³)

V = 4πr³

So the volume of the air is:

V = 24r³ − 4πr³

V = (24 − 4π) r³

Since r = 1.4 inches:

V = (24 − 4π) (1.4 in)³

V ≈ 31.4 in³

5 0

2 years ago

DONT ASK FOR BRAINLIEST

KiRa [710]

2(5k+1)

2x5x2+1 =21
K=2 | 21

2x5x3+1 =31
K=3 | 31

3 0

2 years ago

HI PLS HURRY !!

VARVARA [1.3K]

Step-by-step explanation:

234751

100% sure

Goood luck.

5 0

2 years ago