All categories

2 years ago

Find an equation for the nth term of the arithmetic sequence.

Mathematics

2 answers:

Oksana_A [137]2 years ago

6 0

Answer:

Option B.

Step-by-step explanation:

The given arithmetic sequence is

$-13,-8,-3,2,...$

We need to find the nth term of the given arithmetic sequence.

Here,

First term : $a=-13$

Common difference : $a_2-a_1=-8-(-13)=-8+13=5$

The nth term of an arithmetic sequence is

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

where, a is first term and d is common difference.

Substitute a=-13 and d=5 in the above formula.

$a_n=-13+(n-1)5$

$a_n=-13+5(n-1)$

Therefore, the correct option is B.

vekshin12 years ago

5 0

The answer is the second answer choice, an = -13 + 5(n - 1)

You might be interested in

5x+3y=9 in standard form

tamaranim1 [39]

The standard for is Y=-5/3x +3

8 0

3 years ago

If rectangle ABCD is rotated counter clock wise 90º about the origin, what will be the coordinates of the vertex D'?

7nadin3 [17]

So, the best way to do this is translate it to clockwise. 90 degrees counterclockwise is equal to 270 degrees clockwise. So, basically, to rotate, you would follow the following format for each point-
(X,Y) -> (-Y,X)
Now, you do it for each of the points.
A= (-5,5), so A' would be (-5,-5)
B= (-1,5), so B' would be (-5,-1)
C= (-5,4), so C' would be (-4,-5)
D= (-1,4) so D' would be (-4,-1)
Notice, how all the points end up in the square below it. Each quadrant has a specific number. The top right is quadrant 1, the top left is quadrant 2, the bottom left is quadrant 3, and the bottom right is quadrant 4. If you are rotating 270 degrees clockwise, you move to the right, like a clock. That puts the new rectangle in quadrant 3. That is a way to check your work.
Now, just so you know for future reference, the following are also different formats for different problems--
A 90 degree Clockwise rotation about the origin will be (X,Y) -> (Y, -X) *Note, -x just stands for the opposite. Say your original x is a negative number. Then the prime (new) x will be positive.
A 180 degree Clockwise rotation about the origin would be (X,Y) -> (-X,-Y) *Note, -y also stands for the opposite.
A 270 degree clockwise rotation about the origin would be (X,Y) -> (-Y,X).
For translating---
90 degrees Clockwise = 270 degrees Counter
270 degrees Clockwise = 90 degrees Counter

Hope this helped!

4 0

2 years ago

The sum of two rational numbers is -8 1/4. if one of the numbers is -5 2/3, find the other number. im too lazy to do this

Nataly [62]

Answer:

Step-by-step explanation:

let : x and t this numbers : x +y = -81/4

y == -52/3

x + (-52/3) = -81/4

x = -81/4 + 52/3........continue

4 0

3 years ago

Find the angle between 0° and 360° that is coterminal with a 443° angle.

Yakvenalex [24]

Answer:

If you rotate an angle 360 degrees around, your final angle will be facing the same direction

Thus, the coterminal angle is $443^\circ-360^\circ=83^\circ$

4 0

2 years ago

You go shopping at a local department store with your friend and cousin. You buy one pair of jeans, four pairs of shorts, and tw

VashaNatasha [74]

Answer: Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8

Step-by-step explanation:

Let x= cost per pair of jeans

y = Cost per pair of shorts

z= cost per shirt.

For you, total cost = x+4y+2z= 84

For your friend, total cost = 2x+y+3z=76

For cousin, total cost = x+2y+z= 52

Required system:

$x+4y+2z=84\ (i)\\ 2x+y+3z=76\ (ii)\\ x+2y+z=52\ (iii)$

from (i), $x=84-4y-2z$ (*)

put this in (ii) and (iii) we get

$2\left(84-4y-2z\right)+y+3z=76\\\Rightarrow\ -7y-z+168=76\ (iv)\\\\ 84-4y-2z+2y+z=52\\\Rightarrow\ -2y-z+84=52 \ (v)$

from (iv), $y=-\frac{z-92}{7}\ (vi)$

$\mathrm{Subsititute\:}y=-\frac{z-92}{7}\ \text{in}\ (v)$

$-2\left(-\frac{z-92}{7}\right)-z+84=52\\\\\Rightarrow\ -2\left(-\frac{z-92}{7}\right)-z=-32\\\\\Rightarrow\ -\frac{5z}{7}-\frac{184}{7}=-32\\\\\Rightarrow\ -5z-184=-224\\\\\Rightarrow\ -5z=-40\\\\\Rightarrow\ z=8$