1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pishuonlain [190]
3 years ago
11

Find the 10th partial sum of the arithmetic sequence defined by

Mathematics
2 answers:
Evgesh-ka [11]3 years ago
8 0

Answer:

22.5


Step-by-step explanation:

If you expand the series, you can see the first few terms of the series:

  • Putting 1 in n, \frac{1}{2}(1)-\frac{1}{2}=0
  • Putting 2 in n, \frac{1}{2}(2)-\frac{1}{2}=0.5
  • Putting 3 in n, \frac{1}{2}(3)-\frac{1}{2}=1
  • Putting 4 in n, \frac{1}{2}(4)-\frac{1}{2}=1.5

We can see the series is 0, 0.5, 1, 1.5, ....

This is an arithmetic series with common difference (the difference in 2 terms) 0.5 and first term 0.

We know formula for sum of arithmetic series:

s_{n}=\frac{n}{2}(2a+(n-1)d)

Where,

  • S_{n} denotes the nth partial sum
  • a is the first term (in our case it is 0)
  • n is the term (in our case it is 10 since we want to find 10th partial sum -- sum until first 10 terms)
  • d is the common difference (difference in term and the previous term) (in our case it is 0.5)

Substituting these into the formula, we get the 10th partial sum to be:

s_{10}=\frac{10}{2}(2(0)+(10-1)(0.5))\\s_{10}=5(0+(9)(0.5))\\s_{10}=5(0+4.5)\\s_{10}=5(4.5)\\s_{10}=22.5

So the sum of the first 10 terms is 22.5. Third answer choice is right.


Scilla [17]3 years ago
8 0

Answer is 22.5  so c :)


You might be interested in
Can you tell me the answer please
Andrews [41]

Answer:

11

Step-by-step explanation:

140-129=11

5 0
2 years ago
Read 2 more answers
A real number between 13 and 14
Nataly_w [17]

Answer:

13.6

Hope this helped

3 0
3 years ago
Sharon purchased a used car for $24,600. The car depreciates exponentially by 8% per
Tju [1.3M]

Answer:

The value of car after 5 years of exponentially depreciation is $16,213.36  

Step-by-step explanation:

The initial amount of the car = i = $24,600

The depreciates rate of interest applied = r = 8%

Let The value of car after n years = A  

The number of years = n = 5 years

Now,According to question

The value of car after n years = initial price of car  × (1-\dfrac{\textrm rate}{100})^{\textrm time}

Or, The value of car after 5 years = i × (1-\dfrac{\textrm r}{100})^{\textrm n}

Or, $A = $24,600 × (1-\dfrac{\textrm 8}{100})^{\textrm 5}

Or, $A = $24,600 × (0.92)^{5}

Or, $A = $24,600 × 0.65908

Or, $A = $16,213.36

So, The value of car after 5 years = A = $16,213.36

Hence , The value of car after 5 years of exponentially depreciation is $16,213.36  . Answer

5 0
3 years ago
1. After filling up your car's gas tank with 8.6 gallons, you see that you traveled
alexgriva [62]

Answer:

15.5813 (15.6 miles per gallon)

Step-by-step explanation:

you divide 134 by 8.6 and then round it

8 0
2 years ago
Joselyn saw an alligator that was 5 feet long. How many inches is 5 feet.
goldfiish [28.3K]

Answer:

The alligator is 60 Inches long.

Step-by-step explanation:

5 feet is 60 inches.

hope it helps!

7 0
3 years ago
Read 2 more answers
Other questions:
  • Can somebody answer the equation-1n+1=11
    14·1 answer
  • 20 POINTS!!! A an elevator in a mine is going up and down. The inequality statements compare the elevation of the elevator at th
    11·1 answer
  • Two friends are opening a coffee shop. As they write their business plan, they research the amount of debt similar businesses ca
    6·2 answers
  • 10 mm<br>4 mm<br>u What is the volume of the cone to the nearest whole number?<br>​
    13·1 answer
  • Help, stuck on this math problem!
    5·1 answer
  • You by six notebooks and a backpack. The cost of the backpack is $17.90. You pay 6 dollars in sales tax. Your total bill is $30.
    14·1 answer
  • For what values of x does the graph of f have a horizontal tangent? (Use n as your integer variable. Enter your answers as a com
    11·1 answer
  • What is four plus eight
    8·2 answers
  • Los extremos de un segmento son los puntos A (6, 3) y B (-3, -5), ¿Cuál es la razón “r” en el punto P (-1.2, 3.4) que divide al
    15·2 answers
  • I want a expert or someone that can tell me this %100 I’m offering a brainalist + 20 points
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!