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
Margarita [4]
3 years ago
9

If the sum of the first 12 terms of a geometric series is 8190 and the common ratio is 2. Find the first term and the 20th term.

Mathematics
1 answer:
Reil [10]3 years ago
8 0

The first term is 2 and the 20th term is 1048576 .

<u>Step-by-step explanation:</u>

Here we have , If the sum of the first 12 terms of a geometric series is 8190 and the common ratio is 2. We need to Find the first term and the 20th term. Let's find out:

We know that Sum of a GP is :

⇒ S_n = \frac{a(r^n-1)}{r-1}

So ,Sum of first 12 terms is :

⇒ S_1_2 = \frac{a(2^{12}-1)}{2-1}

⇒ 8190=a(2^{12}-1)

⇒ \frac{8190}{4095}=a

⇒ a=2

Now , nth term of a GP is

⇒ a_n = ar^{n-1}

So , 20th term is :

⇒ a_2_0 = 2(2)^{20-1}

⇒ a_2_0 = (2)^{20}

⇒ a_2_0 = 1048576

Therefore , the first term is 2 and the 20th term is 1048576 .

You might be interested in
The area of a circular sun spot is growing at a rate of 1,200 km2/s.
Tpy6a [65]
A)

\bf \textit{area of a circle}\\\\&#10;A=\pi r^2&#10;\\\\\\&#10;\cfrac{dA}{dt}=\pi \cdot 2r\cfrac{dr}{dt}\implies \cfrac{dA}{dt}=2\pi r\cfrac{dr}{dt}\implies \cfrac{\frac{dA}{dt}}{2\pi r}=\cfrac{dr}{dt}\\\\&#10;-----------------------------\\\\&#10;\left. \cfrac{dr}{dt}  \right|_{r=3000}\implies \cfrac{1200}{2\pi \cdot 3000}=\cfrac{dr}{dt}\\\\

B)

\bf A=\pi r^2\qquad A=490000\implies 490000=\pi r^2\implies \sqrt{\cfrac{490000}{\pi }}=r&#10;\\\\\\&#10;\left. \cfrac{dr}{dt}  \right|_{r=\sqrt{\frac{490000}{\pi }}}\implies \cfrac{1200}{2\pi \cdot \sqrt{\frac{490000}{\pi }}}=\cfrac{dr}{dt}&#10;
8 0
3 years ago
Mrs Brown and Mrs Jones make 4 dozen sandwiches in half an hour in Mrs Jones’ small kitchen. If they had 30 friends in to help,
Pepsi [2]

Answer:

1488 sandwiches in thirty minutes

Step-by-step explanation:

5 0
3 years ago
Help me plz and ty....​
nadya68 [22]

Answer: c

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
The Opera House sells an average of 1,700 tickets per night when the price of each ticket is $25. An employee of the Opera House
irakobra [83]
So here's the solution to the problem:

Calculate the average sell:

1,700 * $25 = $42,500 (revenue)

And if the Opera House wants to increase their revenue:

The price of a ticket will be:

$25 - x (where x is the number of 1-dollar decreases)

The number of tickets in total:

1,700 + 200x

Therefore the equation is:

(1,700 +200x) * ( 25 - x ) = 55,000

We can also solve this equation, but the solutions are not whole numbers.

x 1 = 5.89 and x 2 =10.6

For x = 6 (6 times 1 - dollar decreases):

( 1,700 + 200 * 6 ) * ( 25 - 6 ) = ( 1,700 + 1,200 ) * 18

=2,900 *19 = 55,100 (we will yield the revenue over $55,000)
3 0
3 years ago
What is the value of tan D ?
4vir4ik [10]

Answer:

12/5

Step-by-step explanation:

Tan D = opp/adj = EF/DE = 12/5

8 0
3 years ago
Read 2 more answers
Other questions:
  • Determine whether the system of equations has one solution, no solution, or infinitely many solutions by graphing. If the system
    5·2 answers
  • Carlos gave Lucy 2 more books than she already had. She now has 30 books. How many books did Carlos give Lucy?
    15·1 answer
  • A table and 8 chairs weigh 235.68 pounds in total. If the table weighs 157.84 pounds, how much does ONE chair weigh? Express you
    7·1 answer
  • The measure of angle S is ___ degrees. Round the number to the nearest degree.
    12·1 answer
  • Which is f(5) for the function -2xsquared + 2x -3
    5·1 answer
  • Barbara knows that she will need to buy a new car in 3 years . The car will cost $15000 by then. How much should she invest now
    7·1 answer
  • -7.33 - 1.3n = -0.18<br> HELPPPPP!!!!
    12·2 answers
  • Can someone help me out I need help!
    5·2 answers
  • Please look at the picture and help me with this question
    11·1 answer
  • Ok so this... is confusing the hell outta me any help? <br>​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!