The sum of the first (n) terms of the sequence is given by the formula (given below) . If this sequence is a geometric progression, find q. If this sequence is an Arithmetic progression, find d
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Answer:Example 1:
Find the sum of the first 8 terms of the geometric series if a1=1 and r=2.
S8=1(1−28)1−2=255
Example 2:
Find S10 of the geometric sequence 24,12,6,⋯.
First, find r.
r=r2r1=1224=12
Now, find the sum:
S10=24(1−(12)10)1−12=306964
Example 3:
Evaluate.
∑n=1103(−2)n−1
(You are finding S10 for the series 3−6+12−24+⋯, whose common ratio is −2.)
Sn=a1(1−rn)1−rS10=3[1−(−2)10]1−(−2)=3(1−1024)3=−1023
In order for an infinite geometric series to have a sum, the common ratio r must be between −1 and 1. Then as n increases, rn gets closer and closer to 0. To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r, where a1 is the first term and r is the common ratio.
Example 4:
Find the sum of the infinite geometric sequence
27,18,12,8,⋯.
First find r:
r=a2a1=1827=23
Then find the sum:
S=a11−r
S=271−23=81
Example 5:
Find the sum of the infinite geometric sequence
8,12,18,27,⋯ if it exists.
First find r:
r=a2a1=128=32
Since r=32 is not less than one the series has no sum.
Step-by-step explanation:
Related Questions
If Karen's 45 minute lunch break ended at 12:30 P.M., what time did her lunch break begin?
Answers
Answer:
11:45 PM
Step-by-step explanation:
please mark brainliest :D
Find the length of AN A has coordinates (-4,-7), and N has coordinates (1,5)
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The answer is 13 by using Pythagorean theorem.
The Casey family uses up a 1/2 gallon jug of milk every 3 days. At what rate do they drink milk?
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Answer:
1/6
Step-by-step explanation:
1/2 divided by 3
Simplify each expression by combining like terms.
7a - 6 + 8a
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=7a - 6 + 8
=7a + 8a - 6 =15a - 6
Find the area of the parallelogram ABCD, where DC = 10cm, AD = 6cm, and angle A = 30 degrees
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Answer:
6cm
Step-by-step explanation:
hope this helped
Answer:
60
Step-by-step explanation:
What is i^34?
A. -1
B. i
C. -i
D. 1
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Answer:
A
Step-by-step explanation:
i to an odd power is 1 and i to an even power is -1 so you can see it is A
6. Solve the equation: (c+3)−2c−(1−3c) = 2
a. c=−1 b. c=1 c. c=0 d. c=4
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Answer:
C- C=0
Step-by-step explanation:
A camper leaves camp and travels 4 miles west and 3 miles north. How far is the camper from his original starting point?
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Answer:
5 miles
Step-by-step explanation:
To answer this question, use the following:
According to pythagorean theorem, the hypotenuse of the triangle, c, with legs a and b, can be found with the following equation:
[tex]a^2+b^2=c^2[/tex]
Thus plugging in 3 for a and 4 for b:
[tex]c^2 = 25[/tex]
[tex]c=5[/tex]
A track team has 25 runners. There are 18 boys on the team. What percent of the track team are girls? *
Answers
Answer:
28%
Step-by-step explanation:
Given that,
The total no of runners = 25
No. of boys in the team = 18
We need to find the percent of the track team are girls.
Total no of girls = 25-18 = 7
Percent of girls :
[tex]g=\dfrac{\text{No. of girls}}{\text{Total runners}}\times 100\\\\=\dfrac{7}{25}\times 100\\\\=28\%[/tex]
Hence, there are 28% of girls.
Jordan went shopping last weekend and bought a pair of shoes. The shoes were originally priced at $124.00, but are now on sale for 30% off the regular price. The sales tax is 7%.
What is the sales tax?
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Answer:
8.68
Step-by-step explanation:
just multiply 124.00 times 0.07 and that's it
A 2-digit number is written on a paper. What is the probability that it starts with 2?
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Answer:
1 out of 9
Step-by-step explanation:
Choose the correct solution for this equation X/2-12 = 24
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Answer:
[tex]x=72[/tex]
Step-by-step explanation:
[tex]\frac{x}{2} -12=24[/tex]
[tex]x-24=48[/tex] (multiply [tex]2[/tex] on both sides)
[tex]x=72[/tex]
Hope this helps :)
Mr. Jacobs wants to save over $3,400 for a car. He has a savings account balance of $800 and will make equal weekly deposits for the next 25 weeks.
How much money should Mr. Jacobs deposit each week?
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Answer:
64$
Step-by-step explanation:
25 POINTS and Brainliest
Answers
Answer:$293.83
Step-by-step explanation:
Answer:
293.83$
Step-by-step explanation:
total withdrawals = 6*15.72=94.32$
the rest amount before depostit is 153-94.32=58.68$
the rest amount After depostit is 58.68+235.15=293.83$
Find the equation of the line y=___x+___
Answers
Answer:
y = 3x + 3
Step-by-step explanation:
...............................
Directions
1.Make sure to put the question number next to each answer.
2. If you correctly fill out the questions you will be given a link to 50 points.
3. If you incorrectly answer the question (put random numbers or letters) I will report you.
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Also you will be sent the link within 5 mins of the time you answered the question.
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Okay
convert 1/15 into a decimal correct to 2 decimal places
Answers
Answer:
[tex]\frac{1}{15} = 0.\overline{66}[/tex]
Step-by-step explanation:
We proceed to show the procedure to calculate the given fraction into a decimal form:
1) Since numerator is less than denominator, the integer component of the decimal number is zero:
[tex]\frac{1}{15} = 0.xx[/tex]
2) We multiply the numerator by 10 and find the tenth digit:
[tex]\frac{10}{15} = 0[/tex]
Then,
[tex]\frac{1}{15} = 0.0xx[/tex]
3) We multiply the fraction in 2) by 10 and find the hundredth digit:
[tex]\frac{100}{15} = 6[/tex]
Then,
[tex]\frac{1}{15} = 0.66x[/tex]
And the remainder is:
[tex]r = 100-15\times 6[/tex]
[tex]r = 10[/tex]
4) We multiply the remainder by 10 and divide this result by the denominator to determine the thousandth digit:
[tex]\frac{100}{15} = 6[/tex]
Then,
[tex]\frac{1}{15} = 0.666[/tex]
This question asks us to write a decimal correct to 2 decimal places, which has the characteristic that is infinite periodical decimal. Then, the result correct to 2 decimal places is:
[tex]\frac{1}{15} = 0.\overline{66}[/tex]
Brian agrees to watch his neighbor’s dogs for 7 days. His neighbor provides a 128-ounce bag of dog food. Buster eats 20.5 ounces in 2 days and Roxy eats 22.5 ounces in 3 days. Does Brian have enough food to feed the dogs all 7 days? Explain.
Answers
Answer:
Yes, he has exactly the right amount
Step-by-step explanation:
Buster- 20. 5 = 2 days 20.5+20.5+20.5+10.25= 71.75 for 7 days
Roxy- 22.5= 3 days 22.5+22.5+11.25=56.25 for 7 days
71.75+56.25= 128oz
Brian will have exactly enough food for 7 days
What is the ordered pair for point B?
Answers
Answer:
(4,2)
Step-by-step explanation:
..................................
Maria paid $240 for a table set after a discount of 40%. What was the original price?
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Answer:
The original price was 400 dollars.
Step-by-step explanation:
400 times 0.4 equals 160. 400 minus 160 equals 240. Therefore the answer is 400 dollars.
Given that 9=110 8=70 an p is parallel to q did I fill this out right?
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Answer:
yes i think so it looks quite accurate
Answer:
This does look like the right answer. I think you filled it out right
Step-by-step explanation:
where does the line cross in the equation y=2x=12
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What is the answer for this
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Answer:
the product of 5 and a number
Step-by-step explanation:
product is the result of a multiplication problem
5c is the same as 5 times c
we don’t write an x (5xc) because x is sometimes used as a “placeholder” instead of c
I need help with this assignment problem, pls help ;-;
Answers
Answer:
1090 miles
Step-by-step explanation:
50525 - 48345 = 2180 miles in the two weeks
2180/2 (to find out how many miles in 1 week) = 1090
50525- 48345= 2180 divided by 2 equals 1090
Which equation is equivalent to the equation 6x + 9=12
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Answer:
the answer is 1/2
Step-by-step explanation:
i solved it
PLEASE ANSWER I WILL MARK YOU BRAINLIEST!!!
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9514 1404 393
Answer:
distributesubtractadddivide byStep-by-step explanation:
[tex]\begin{array}{rccl}&-2(5x+8)=14+6x\\\text{Step 1:}&-10x-16=14+6x&\text{distribute}&\text{-2 to $5x$ and 8.}\\\text{Step 2:}&-16x-16=14&\text{subtract}&6x\\\text{Step 3:}&-16x=30&\text{add}&16\\\text{Step 4:}&x=\dfrac{30}{-16}&\text{divide by}&-16\end{array}[/tex]
At each step after the first, we use one of the properties of equality to simplify the equation. In the first step, we use the distributive property to eliminate parentheses.
_____
Additional comment
Note that the first step could have been "divide by -2", which would result in the equation 5x+8 = -7 -3x. Subsequent steps would add 3x, subtract 8, and divide by 8, to give a result of x=-15/8. There is usually more than one way to work a math problem.
I will give brainliest
Answers
Answer: 16 quarts of blue paint
Step-by-step explanation:
i divided 3 by 24 to see how many quarts there was then took the answer which is 8 and multiplied it by 2.... i dont know if its right but i tried
2x + 6 = 8
can someone tell me dis
Answers
Answer:
x=1
Step-by-step explanation:
is the answer
Answer:
x = 1
Step-by-step explanation:
What is the approximate circumference of a circle with the diameter of 9
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Answer:
9pi
Step-by-step explanation:
circumference is 2(pi)(r) or diameter(pi)
Latoya made 2 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for both necklaces was $8.40. If the beads cost $2.70 for each necklace, how much did each ppendant cost
I'll give brainiest if correct :)
Answers
Answer:
its 2.60 for each pendent