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frez [133]
3 years ago
9

The third term of an arithmetic sequence is 14 and the 9th term is -1. Find the first four terms of the sequence.​

Mathematics
1 answer:
Liula [17]3 years ago
4 0

Answer:

The first four terms of the sequence are :  19, 16.5 , 14 , 11.5

Step-by-step explanation:

In the given sequence:

a(3) =  14, a(9)  = -1

The general term of a sequence in Arithmetic Progression is:

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

a(3) = a + (3 -1) d = a + 2 d

and a(9) = a + (9- 1 ) d = a  + 8 d

⇒   a + 2 d =  14      .........  (1)

and a + 8 d  = -1    ...........  (2)

Now, solving the given system of equation, we get:

From (1), a  = 14 - 2 d

Put in (2), we get:

a + 8 d  = -1                ⇒   14 - 2 d + 8d = -1

⇒  14 +   6d   = -1  

or,  6d = -1 -14 = -15

⇒  d = -15/6 = -2.5

or, d  = -2.5

Then a  = 14 - 2 d = 14 - 2(-2.5)  =14 + 5  = 19, or a  = 19

Now, first four terms of the sequence is:

a = 19

a(2) = a + 4 = 19 - 2.5 = 16.5

a(3) = a + 2d = 19 + 2(-2.5) = 19 - 5 = 14

a(4) = a  + 3d = 19 + 3(-2.5)  = 19  - 7.5  = 11.5

Hence, the first four terms of the sequence are :  19, 16.5 , 14 , 11.5

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We know gas is $2.79 a gallon so we multiply 2.79 (cost per gallon) x 12.34 ( our total gallons used) =$34.43 in gasoline.

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A 12-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on the level ground 7 f
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Answer:

the ladder reaches up to 9.75 ft. high

Step-by-step explanation:

a^2+b^2=c^2

plug in the numbers

a^2+49=144

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3 0
3 years ago
Read 2 more answers
if a shoelace drawer is 12.49 inches and a paperclip drawer is 4.579 inches about how many inches wider is the shoelace drawer t
sammy [17]

The shoelace drawer is 7.911 inches wider than the paperclip drawer.

<h3>Measurement difference between two drawers</h3>

The height of shoelace drawer is = 12.49 inches

The height of paperclip drawer is = 4.579 inches

Therefore the measurement difference between the two drawer is = 12.49 inches - 4.579 inches

= 7.911 inches

Therefore, the shoelace drawer is 7.911 inches wider than the paperclip drawer.

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brainly.com/question/25770607

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7 0
2 years ago
Please help im really confused<br><br> Which expression is equivalent to 4(7 + 8)?
Hatshy [7]

Answer:

With the answer choices:

A. 11 + 8

B. 11 + 12

C. 28 + 12

D. 28 + 32

The answer would be 28+32.

Step-by-step explanation:

Use the distributive law.

4 * 7 = 28

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Hope this helps!

8 0
3 years ago
Can someone help me with number 4,5 and 6?
True [87]
4) You know slope-intercept form is y=mx+b. So using these two given points, you can find the slope! 

(-8,5)  (-3,10) [Use the y1-y2 over x1-x2 formula to solve for slope]

10 - 5         5
---------   = ----- = 1 
-3-(-8)         5

Hurray! You got a slope of one. Now substitute this back into your original equation:
y=mx+b --> y=1x+b 

Next, we find what our "b" is, or what our y-intercept is:
Using one of the previous points given, substitute them into the new equation:
[I used the point (-3, 10) ]

y=1x+b
10=1(-3)+b  SUBSTITUTE 
10=-3+b     MULTIPLY
10=-3+b
+3   +3    ADD
----------
13=b     SIMPLIFY 

So, now we have our y-intercept. Use this and plug it into the equation:
y=1x+b --> y=1x+13 

y=1x+13 is our final answer.



5) So for perpendicular lines, your slope will be the opposite reciprocal of the original slope. (Ex: Slope is 2, but perpendicular slope is -1/2) 

We have the equation y= 3x-1, so find the reciprocal slope! 
--> y=-1/3x-1 

Good! Now we take our given point, (9, -4) and plug it into the new equation:

y=-1/3x-1
-4=-1/3(9)+b   SUBSTITUTE and revert "-1" to "b", for we are trying to find the y-     -4=-3+b          intercept of our perpendicular equation. 
+3   +3            ADD
--------
-1=b    SIMPLIFY 

So, our final answer is y=-1/3x+(-1)

6) I don't know, sorry! :( 
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3 years ago
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