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
insens350 [35]
3 years ago
12

Find the sum of the geometric series 40 + 40(1.005) + 40(1.005)^2 + ⋯ + 40(1.005)^11.

Mathematics
1 answer:
KiRa [710]3 years ago
4 0

Answer:

The sum is 493.4

Step-by-step explanation:

In order to find the value of the sum, you have to apply the geometric series formula, which is:

\sum_{i=1}^{n} ar^{i-1} = \frac{a(1-r^{n})}{1-r}

where i is the starting point, n is the number of terms, a is the first term and r is the common ratio.

The finite geometric series converges to the expression in the right side of the equation. Therefore, you don't need to calculate all the terms. You can use the expression directly.

In this case:

a=40

b= 1.005

n=12 (because the first term is 40 and the last term is 40(1.005)^11 )

Replacing in the formula:

\frac{a(1-r^{n})}{1-r} = \frac{40(1-1.005^{12})}{1-1.005}

Solving it:

The sum is 493.4

You might be interested in
How to write 532÷4 in place valve
storchak [24]
First, divide. 532 divided by 4 equals 133. 1 is in the hundreds place, 3 is in the tens place, 3 is in the ones place
3 0
3 years ago
Find c. Round to the nearest tenth
sergeinik [125]

Answer:

c = <u>0.5 cm</u>

Step-by-step explanation:

Using the Sine rule in the triangle, then

=  ( cross- multiply )

c × sin105° = 2 × sin15° ( divide both sides by sin105°

c =  ≈ 0.5 cm ( to the nearest tenth )

8 0
3 years ago
Jack puts the letters of the word BUILDING on pieces of paper and puts the pieces in a bag. He draws two letters without looking
Zepler [3.9K]

there are 8 letters

2/8 to get i on the first draw

1/7 to get i on the second draw (no replacement)

2/8 * 1/7 = 2/56

1/28


The probability is 1/28

5 0
3 years ago
If y varies directly as x and y-21 when x<br> is 7, find x when y = -5.
klasskru [66]

Step-by-step explanation:

Since, y varies directly as x:

\therefore \: y = kx..(1) \\ (k = constant \: of \: proportionality) \\ at \: y = 21 \: and \: x = 7 \\ 21 = k \times 7 \\ k =  \frac{21}{7}  = 3 \\ plugging \: k = 3 \: in \: equation \: (1) \\ y = 3x..(2) \\ plugging \:  \: y =  - 5  \: in \: (2)\\  - 5 = 3x \\ x =  \frac{ - 5}{3}  \\   \:  \:  \:  \:  \:  \: \huge \red{ \boxed{x =  -  \frac{5}{3} }}

6 0
3 years ago
Read 2 more answers
2-10n more math homework :|
creativ13 [48]

Step-by-step explanation:

Yea we need more information.

4 0
3 years ago
Other questions:
  • A cookie recipe states for every 3 cups of flour, 1 1/2 teaspoons of vanilla are needed. How many teaspoons are needed for 5 cup
    9·1 answer
  • What is the equation of the line that is perpendicular to the
    5·1 answer
  • Which statement is true about credit cards?
    14·1 answer
  • Volunteers were 3/4 finished with the walkathon when they reached the 4 1/2 kilometer mark.How long was the walkathon
    15·1 answer
  • Find the average rate of change of a function that contains the points (-2,3) and (2,5).
    6·1 answer
  • Cody's Cafe uses 1 7/10 bags of coffee every day. How many days will 6 4/5 bags of coffee last?
    11·1 answer
  • AABC is rotated 90° clockwise to create AA'B'C'. Which of the following transformations would also map B to B'?
    9·1 answer
  • 2x-8=x+17<br> I need help
    5·2 answers
  • Prove &lt;4 and &lt;1 are supplementary.
    9·2 answers
  • Given ΔBCD where B(2,1), C(3,4), and D(4,1), reflect over the line y=1.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!