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german
3 years ago
7

"Find the sum of the first 50 term in this sequence 4, 7, 10, 13, ...". How do i do this without writing them all out, and how d

o i develop a formula?
Mathematics
1 answer:
melisa1 [442]3 years ago
5 0
First term ,a=4 , common difference =4-7=-3, n =50
sum of first 50terms= (50/2)[2×4+(50-1)(-3)]
=25×[8+49]×-3
=25×57×-3
=25× -171
= -42925
derivation of the formula for the sum of n terms
Progression, S
S=a1+a2+a3+a4+...+an

S=a1+(a1+d)+(a1+2d)+(a1+3d)+...+[a1+(n−1)d]   →   Equation (1)

S=an+an−1+an−2+an−3+...+a1

S=an+(an−d)+(an−2d)+(an−3d)+...+[an−(n−1)d]   →   Equation (2)

Add Equations (1) and (2)
2S=(a1+an)+(a1+an)+(a1+an)+(a1+an)+...+(a1+an)

2S=n(a1+an)
S=n/2(a1+an)

Substitute an = a1 + (n - 1)d to the above equation, we have
S=n/2{a1+[a1+(n−1)d]}
S=n/2[2a1+(n−1)d]
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Evelyn can run 3 miles in 40 minutes
hram777 [196]

Answer:

m= 4.5 miles

Step-by-step explanation:

Let the number of miles Evelyn can run be m and can be modeled by the equation below

m= kx

Where x Is the Minutes

When m= 3

x= 40

3= k40

k= 3/40

If x= 60

m=3/40(60)

m = (60*3)/40

m= 180/40

m= 4.5 miles

5 0
2 years ago
Help I need sleep and I live in Canada, de las ovejas and it's 1am
MrMuchimi

Answer:

Answer:

The student council made more snow cones per hour than the parent volunteers.

Explanation:

To find the number of snow cones made per hour:

XXX

Divide the number of snow cones made

XXX

by the number of hours spent making snow cones.

Parent volunteers

XXX

Number of snow cones:  

120

XXX

Number of hours spent making snow cones:  

5

Number of snow cones per hour:  

120

÷

5

=

24

Student council

XXX

Number of snow cones:  

100

XXX

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4

Number of snow cones per hour:  

100

÷

4

=

25

Since the student council made  

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snow cones per hour and the parent volunteers only made  

24

snow cones per hour:

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Step-by-step explanation:


4 0
3 years ago
A carpenter is assigned the job of expanding a rectangular deck where the width is one-fourth the length. The length of the deck
leva [86]
Let the width be W, then the length is 4W (since the width is 1/4 the length)

The area of the original deck is W*4W=4W^{2}

The dimensions of the new deck are :

length = 4W+6
width=W+2

so the area of the new deck is :

(4W+6)(W+2)= 4W^{2}+8W+6W+12= 4W^{2}+14W+12

"<span>the area of the new rectangular deck is 68 ft2 larger than the area of the original deck</span>" means that we write the equation:

4W^{2}+14W+12=68+4W^{2}

14W+12=68

14W=68-12=56

W= \frac{56}{14}= 4

the length is 4W=4*4=16    ft


Answer: width: 4, length: 16
3 0
3 years ago
What is the arc measure, in degrees, of major arc \stackrel{\large{\frown}}{ADC} ADC ⌢ A, D, C, start superscript, \frown, end s
Mrrafil [7]

Answer:

\stackrel{\large{\frown}}{ADC}    = 186^{\circ}

Step-by-step explanation:

Given

See attachment

Required

Determine the measure of \stackrel{\large{\frown}}{ADC}

The\ sum\ of\ angles\ in\ a\ circle\ is 360^{\circ}.

So, we have:

\stackrel{\large{\frown}}{ADC} + \stackrel{\large{\frown}}{APB}  + \stackrel{\large{\frown}}{BPC}  = 360^{\circ}

Where:

\stackrel{\large{\frown}}{APB}  = 70^{\circ}

\stackrel{\large{\frown}}{BPC}  = 104^{\circ}

Substitute these values in the above equation.

\stackrel{\large{\frown}}{ADC} + 70^{\circ}   +104^{\circ}   = 360^{\circ}

\stackrel{\large{\frown}}{ADC} + 174^{\circ}   = 360^{\circ}

Collect Like Terms:

\stackrel{\large{\frown}}{ADC}    = 360^{\circ} - 174^{\circ}

\stackrel{\large{\frown}}{ADC}    = 186^{\circ}

7 0
3 years ago
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GalinKa [24]

9514 1404 393

Answer:

  x = 5

Step-by-step explanation:

These points have the same x-coordinate, so are on the same vertical line:

  x = 5

6 0
3 years ago
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