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
HailyDenney2 I need your assistance please!
ExtremeBDS [4]

Answer:

60 x 35 = 2,100

609,000 / 2,100 = 290 km ^ 2

Step-by-step explanation:

3 0
3 years ago
Hence find the value of x that satisfies the two equations y =
sammy [17]

Answer:

x=6

Step-by-step explanation:

since y=5x/2-7, and y=4x/3

         so 5x/2-7=4x/3

              5x/2-4x/3= 7

              15x-8x/6=7

               7x/6=7

               x= 7*6/7= 6

5 0
2 years ago
Determine the maximum number of zeros of the polynomial function -8x^4-x^2+2 a. 1 c. 3 b. 4 d. 2 Please select the best answer f
alexgriva [62]
Generally speaking, the number of solutions to an algebraic equation is equal to the exponent of the highest power.  so the answer is b.4


6 0
3 years ago
The denominator of a fraction is 4 more than the numerator if both are decreased by 3 the simplified result is 6/7 find original
Hitman42 [59]

<u>Answer:</u>

The denominator of a fraction is 4 more than the numerator. The original fraction is \frac{27}{31}

<u>Solution:</u>

Given that  

Denominator of fraction is 4 more than the numerator.

Let’s say numerator of fraction be represented by variable x.

So denominator of a faction as it is four more that numerator will be x + 4

Also given if both decreased by three than simplified result is \frac{6}{7}

=>\frac{(x-3)}{((x+4)-3)}=\frac{6}{7}

Solving above equation for x

=> 7(x – 3  ) = 6 ( x + 1 )

=> 7x – 21 = 6x + 6

=> 7x – 6x = 6 + 21

=> x = 27

Numerator of fraction = x = 27

Denominator of fraction = x + 4 = 27 + 4 = 31

\text {required fraction}=\frac{\text {numerator}}{\text {denominator}}

= \frac{27}{31}

Hence the original fraction is \frac{27}{31}

7 0
3 years ago
Tim walks 2/3 mile to school each day.He walks the same distance home. how far does he walk to and from school during a regular
klio [65]
About 6.7 miles for a week
5 0
3 years ago
Read 2 more answers
Other questions:
  • Least to greatest 2.614;2.146;2.46;2.164
    13·2 answers
  • Suppose Caryl could spend up to $30, what is another possible combinations of cupcakes and brownies that she could buy? How coul
    11·1 answer
  • To decorate her bedroom, Lisa spent $62.89 on new bedding, $48.26 on paint, and $81.99 on accessories. About how much did she sp
    9·2 answers
  • ∠x and ∠y are supplementary angles. ∠y Measures 116੦. What is the measure of ∠x?
    12·1 answer
  • A standard die is rolled three times. What is the probability of rolling a number less than 5 on all three rolls?
    6·1 answer
  • ВС<br> Round your answer to the nearest hundredth.<br> B.<br> ?<br> 35°<br> A<br> 2.<br> с
    13·1 answer
  • Let a Δ b = (a+b)2+5. what is 1 Δ - 4?
    9·1 answer
  • Evaluate the expression when n=6<br> n² – 5n-2
    11·2 answers
  • 70x + 50 = 190<br> What is x?
    13·2 answers
  • Factor problems 9 - 12 by using the difference of squares method.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!