Use sigma notation to represent the sum of the first six terms of the following sequence: −10, −13, −16, …
Answers
Answer:
c
Step-by-step explanation:
i took the test and got it right so... and do you have Mr. Hoffman
The sum of the first six terms of the following sequence is ∑(from i=1 to 6) (-10 - 3(i-1)), the correct option is A.
What is the sum of terms of a geometric sequence?Lets suppose its initial term is f=a , multiplication factor is r
and let it has total n terms, then, its sum of a geometric sequence is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
We are given that;
The sequence; −10, −13, −16, …
Now,
The given sequence is an arithmetic sequence with first term (a1) = -10 and common difference (d) = -3.
Using this formula, we can find the first six terms of the sequence as follows:
a1 = -10
a2 = -10 + (-3) = -13
a3 = -10 + 2(-3) = -16
a4 = -10 + 3(-3) = -19
a5 = -10 + 4(-3) = -22
a6 = -10 + 5(-3) = -25
We can represent the sum of the first six terms using sigma notation as:
∑(from i=1 to 6) ai = (-10) + (-13) + (-16) + (-19) + (-22) + (-25) = -105
The sum of the first six terms of the given sequence is -105.
Using sigma notation, we can write this as:
∑(from i=1 to 6) (-10 - 3(i-1)) = -105
Therefore, by the geometric sequence the answer will be ∑(from i=1 to 6) (-10 - 3(i-1)).
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Related Questions
Alexa earns $63,000 per year. What is her monthly salary a) $8,000 b) $4,500 c) $5,250 d)$6,320
Answers
Answer:
$5,250 C
Step-by-step explanation:
All you do is $63,000 divided by the 12 months in a year. Then you get your answer of $5,250
Look at the attached picture
Hope it will help you
Plz help fast will give brainiest
Answers
Answer:
X has to be 6 or anything bigger than that.
Step-by-step explanation:
18-12=6
Hope this helped
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me!!
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hello I'm stuck on these if someone helped me and told me how to do it I would be so happy :D
Answers
Answer:
see explanation
Step-by-step explanation:
To find the first 4 terms, substitute n = 1, 2, 3, 4 into the sequence rule.
For the 10 th term substitute n = 10 into the sequence rule
(a)
n = 1 → 1² + 3 = 1 + 3 = 4
n = 2 → 2² + 3 = 4 + 3 = 7
n = 3 → 3² + 3 = 9 + 3 = 12
n= 4 → 4² + 3 = 16 + 3 = 19
n = 10 → 10² + 3 = 100 + 3 = 103
Thus the first 4 terms are 4, 7, 12, 19 and term 10 is 103
------------------------------------------------
(b)
n = 1 → 2 × 1² = 2 × 1 = 2
n = 2 → 2 × 2² = 2 × 4 = 8
n = 3 → 2 × 3² = 2 × 9 = 18
n = 4 → 2 × 4² = 2 × 16 = 32
n = 10 → 2 × 10² = 2 × 100 = 200
Thus the first 4 terms are 2, 8, 18, 32 and term 10 is 200
Brian and Katie have $40 to spend at the store.
If they get 4 bags of pasta which cost $1 each,
2 cans of tomatoes which cost $2 each, a $3
gallon of milk, and 3 loaves of bread which
cost $3 each, how much change will James
and Kelly receive after their purchase?
$
Answers
Answer:
It would be 20
Step-by-step explanation: 4x1=4+2x2=4+3+3x3=9 final answer 40-20=20
A skate board was originally priced at £100 on Thursday.
On Friday the price was reduced by 50%. On Saturday, Friday's price was reduced by a further 30%. On Sunday, Saturday's price was reduced by a final 10%.
What was the final percentage reduction on the original price?
Answers
Answer:
31.5
Step-by-step explanation:
50 percent of 100 would be 50, so you subtract 50 from 100, and 30 percent of 50 is 15, so you subtract 15 from 50 and then get 35, which 10 percent of is 3.5, and finally you subtract 3.5 from 35 and you end up with 31.5.
ANSWER ASAP PLEASE!
(02.01)A class has 4 boys and 10 girls. What is the ratio in simplest form that compares number of boys to total number of students?
4:14
4:10
2:7
2:5
Answers
Answer:
2:7
Step-by-step explanation:
4+10=14
The least common factor is 2.
4/2=2
14/2=7
Answer:
c. 2:7
Step-by-step explanation:
4+10 is 14
2 is the least common factor
4/2 simplified to 2
14/2 simplified to 7
plz help i need this asap
Answers
Answer:
option B
Step-by-step explanation:
How do you find the area of composite shapes with rectangles and triangles?
Answers
The area of a rectangle: Base times Height
The area of a triangle: (1/2) times Base times Height.
Happy to help!
Which fraction represents 25% of the offspring in a genetic cross?
Answers
Answer:
1/4
Step-by-step explanation:
There should be 4 boxes in a genetic cross
Answer:
1/4 because we already know that 1/4 is equal to 25%
Step-by-step explanation:
PLZZZZ I NEEED HELP!!!
I said please
Answers
Step-by-step explanation:
Angle 128 ° + Angle Y = 180 °
Y = 180 - 128
= 52 °
5x + 3 + Y = 180
5x + 3 + 52 = 180
5x + 55 = 180
5x = 180 - 55
5x = 125 °
x = 125 ÷ 5
x = 25
1. Carol puts $5.50 in her piggy bank each week. She has been doing this for 15 weeks. How much has she saved?
2.Buttons come in packs of 12. How many packs should you buy if you need 50 buttons?
3.The florist puts 8 flowers in a vase. How many vases can she fill completely if she has 75 flowers?
4.Caleb bought a t-shirt at the Aquarium for $7.99. He gave the clerk $10. How much change did he receive?
Answers
2. You need to buy 5 packs of buttons since 5 packs is 60 and 4 is 48. And more buttons is better then less
1. 4x - 5 ( for x is 4 )
2. 2a + 5 ( for a is 3 )
3. 6(n-5) + 3 ( for n is 9 )
4. 2( 3y - 2) for y is 2
Answers
Answer:
11
12
24
16
substitute variable for the number and solve
2. 11
3. 27
4. 8
What is the circumference of the circle? Use 3.14 for pi
d= 33 cm
Answers
Answer:
103.62 cm
Step-by-step explanation:
c=pid
3.14(33)=103.62
Answer:
circumference = 2πr (r = d/2)(r=16.5)
=2×3.14×16.5
=103.62
Step-by-step explanation:
HOPE IT HELPS YOU
Please Answer !! A store is having a sale on almonds and jelly beans. For 5 pounds of almonds and 3 pounds of jelly beans, the total cost is $23. For 2 pounds of almonds and 6 pounds of jelly beans, the total cost is $20. Find the cost for each pound of almonds and each pound of jelly beans.
Answers
Answer:Let x = number of pounds of jelly beans
y = number of pounds of almonds.
Then, 4x + 8y = 33
2x + 3y = 13
Multiply the second equation by -2 to get the system:
4x + 8y = 33
-4x - 6y = -26
Adding the equations, we get 2y = 7. So, y = 3.5
Substitute for y in either of the given equations: 2x + 3(3.5) = 13
2x + 10.5 = 13
2x = 2.5
x = 1.25
The kitten weighs 3 pounds. How many ounces does it weigh?
0>) 48 ounces
1) 60 ounces
(3) 19 ounces
) 30 ounces
Answers
Answer:
the first one
Step-by-step explanation:
1 pound equals 16 ounces.
The total number of ounces that it will weight is 48.
What are ounces ?"The ounce is the name of several different units of mass, weight or volume and is derived almost unchanged from the uncia, an Ancient Roman unit of measurement.
The avoirdupois ounce (exactly 28.349523125 g) is 1⁄16 avoirdupois pound; this is the United States customary and British imperial ounce. It is primarily used in the United States to measure packaged foods and food portions, postal items, areal density of fabric and paper, boxing gloves, and so on, but it is sometimes also used elsewhere in the Anglosphere."
Given,
Number of pounds = 3
[tex]1 pound = 12 ounces[/tex]
So, 3 pound = 12*3 = 48 ounces
Hence, option A is the correct option.
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FOR FAST BRAINLIEST limited time only !!! ASAP!!
Easy math, draw a picture of it, the chart !!
Answers
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
hi!
got a question!
I couldn't understand this, so please try your best understanding me
The question is : Find the volume of the figure above
Answers
Answer:
985.31 cm² is the volume of the figure.
Step-by-step explanation:
First, find the volume of the cylinder
[tex]V=\pi r^{2} h[/tex] Use this equation to find the volume of the cylinder
[tex]V=\pi (4)^{2} (20)[/tex] Simplify the exponent and multiply
[tex]V = 320\pi[/tex] Multiply
1005.31 cm² is the volume of the cylinder
Next, find the volume of the rectangle
V = L x W x H Use this equation to find the volume of the rectangle
V = 20 x 1 x 1 Multiply
V = 20 cm² is the volume of the rectangle
Subtract the volume of the rectangle from the volume of the cylinder to find the volume of the figure.
1005.31 cm² - 20 cm² = 985.31 cm² is the volume of the figure.
If this answer is correct, please make me Brainliest!
Answer:
I had 271.36cm^3
Step-by-step explanation:
There are 2 figures in the diagram above a cylinder and a cuboid if I'm right
So volume of Figure = V(cylinder) + V(cuboid)
V(cylinder) =pi x rxr xh
Pi=3.142, radius is 2 (since diameter is 4cm), height is 20cm.
So V(cylinder) =3.142x4x20 = 251.36cm^3
V(cuboid) =lbh =1x1x20 =20cm^3
So V(figure)= 20+251.36
=271.36cm^3
ANSWER QUICKLY PLEASE
Answers
Answer:
0,4 meters
Step-by-step explanation:
1. 0,08 x 2 = 0,16 m² (area of the square)
2. √0,16 = 0,4 m (length of one side)
Answer:
00.08 meters
Step-by-step explanation:
growup0.8 32-6=6
Need help with this please
Answers
Answer:
6.157
-1.009
5.148
If Candace made a scatter plot of the math scores of eighth-grade students (vertical scale) and their heights in inches (horizontal scale), what type of line of best fit should she expect the scatter plot show?
A. a line with positive slope
B. a line with negative slope
C. a horizontal line
D. There would be no line of best fit.
Answers
Answer:
The correct option is (D).
Step-by-step explanation:
A scatter plot is a mathematical graph used to display the linear relationship between two variables.
Points are plotted on the graph and a line of best is drawn to represent the linear relationship between the two variables.
If the line is upward moving this implies that there is positive relation between the variables.
If the line is downward moving this implies that there is negative relation between the variables.
If there is no line of best fit that can be formed using the data provided then this implies that there is no linear relationship between the variables.
The variables math-score and height of the students has no relation between them. This is because the height of a student does not factor the score he/she received in their math exam.
So, the scatter plot for this data will not have a line of best fit.
Thus, the correct option is (D).
simplify the expression:
20m^3
over
32m^5
Answers
Answer:
5 over 8m ^2
Step-by-step explanation:
20m^3
32m^5
m^3 divided by m^5 equals one over m^2.
20 divided by 32 is 5 over 8.
Multiply these and you'll get 5 over 8m^2
Answer:
0.00023841857
125/524288
Step-by-step explanation:
Decimal form: 0.00023841857
Fraction Form: 125/524288
Using the paystub, how much will Karla’s paycheck be written for?Pay Stub Q1 Question 1 options: a) $260.00 b) $25.73 c) $200.20 d) 4019
Answers
Answer:(b)
Step-by-step explanation:
Sasha makes a wooden base for a sculpture with the dimensions shown.
The sculpture is too heavy for the base, so she needs to add a brace from
point C to point E to make the base stronger.
How long does the brace need to be? Round your answer to the nearest tenth.
a) 3.4 ft
b) 4.6 ft
c) 5.4 ft
d) 9 ft
Answers
what is the solution
x/9+7≥10
Answers
Answer:
x≥27 or A
Explanation:
Well, I just used photo math, hope it helps!
What is the relationship between the diameter and radius?
(1 Point)
d=r2
2r=d
2d=r
O
rxr=d
Answers
Answer:
2r = d
Step-by-step explanation:
Diameter is two times of radius.
Diameter = 2 x radius
2 r = d
Hey guys I really need help with this one exercise soo maybe can someone plzz help for 20 points? Write also the whole detail of your answer plz!
Math problem: There are 36 carpenters in a crew. On a certain day, 29 were present. What percent showed up for work? (round to the nearest tenth)
Answers
Answer:
10%
Step-by-step explanation:
Answer:
The percentage showed up for work is 8.556 %
● Given that total number of Carpenters is 36.
● On a certain day only 29 carpenters were present.
● To calculate the percentage we have to divide the number of carpenters present on that specific day by the total number of carpenters and multiply the product with 100 i.e., we have to divide 29 with 36 and multiply it with 100.
Percentage = (29 / 36) * 100
= (0.80556) * 100
= 80.556
● Therefore the required percentage is 80.556%
Step-by-step explanation:
HOW IS THE INSCRIBED QUADRILATERAL PROOF WRITTEN?
Answers
Answer:
In the quadrilateral ABCD can be inscribed in a circle, then we have seen above using the inscribed angle theorem that the sum of either pair of opposite angles = (1/2(a1 + a2 + a3 + a4) = (1/2)360 = 180.
Step-by-step explanation:
hope this answers your question
a. 45
b. 30
c. 85
d. 90
Answers
Solve the mathematical puzzle.
Determine the digits of R from these clues.
The first digit is the answer when the third digit is divided by 2.
The second and third digits add to 7.
The second digit minus the first digit is 1.
R is a three-digit number:
243
342
234
432
Answers
Answer:234
Step-by-step explanation:
Just look at the choices and try to find the right one with those features