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
Which is a compound event?
Pepsi [2]

Heads or tails lands 1 time in 1 coin flip

8 0
3 years ago
Read 2 more answers
What is five + five
LekaFEV [45]
Five plus five is ten
6 0
2 years ago
Solve for x.<br> ASAP, please help me
LUCKY_DIMON [66]
The answer to this is 81
4 0
3 years ago
Andrea bought 12 bagels and 10 muffins at the bakery of these items 2/3of the bagels were Multigrain and3/5of the muffins were b
nevsk [136]
Hi there!

If Andrea bought 12 bagels and 2/3 were multigrain we can determine what the total amount of bagels that are multigrain by finding a common denominator. We can do this by multiplying 2/3 * 4 which gets us the common denominator we need.

2/3 * 4 <--- Equation
8/12 <--- Simplified from step 1.

Therefore 8 out of the 12 bagels Andrea bought were multigrain! 
5 0
3 years ago
Please help I don’t <br> understand how to describe the Domain and range of the function
bulgar [2K]

Answer:

domain = {x|xER}

range = {y|y≥0,yER}

Step-by-step explanation:

|x| means the absolute value which in this case is the distance from 0. On a graph this function would look like a v and would mean it would have infinite x-values since it is opening upwards in both directions.

For the range the vertex of this function is (0,0), if the x-coordinate were 0 the y-coordinate would be 0 because the absolute distance from 0 is 0. for another x-coordinate say -2 the absolute distance from 0 is 2 meaning the y-value is 0 since y=|x|, making the coordinate (-2,2) meaning the range is every y value must be above 0 since there is no way for the y-value to be negative

3 0
3 years ago
Other questions:
  • Lin has picked 1 ½ cups of raspberries, which is enough for ¾ of a cake. How many cups does she need for the whole cake?
    8·1 answer
  • What is the solution set of {x | x &lt; -3} ∩ {x | x &gt; 5}
    8·1 answer
  • Could you show an example of the problem?<br> Use a number line to solve 235 + 123
    13·1 answer
  • Find how much was invested
    6·1 answer
  • A polynomial of degree 4 in y has at most
    10·2 answers
  • Please help as soon as possible???<br><br> All of the following are equivalent except???
    10·1 answer
  • What is the domain of the function represented by this graph
    12·1 answer
  • Suppose you want to throw a party. you have $214 to spend. so far you have purchased 5 decorations that each cost d dollars. whi
    13·2 answers
  • What is the slope of the line passing through the points (-3, 4) and (2, -1)
    12·2 answers
  • What is the equation of the line that passes through the point (-2,-2) and has a<br> slope of 22
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!