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
pickupchik [31]
2 years ago
8

How many terms are there in a geometric series if the first term is 4, the common ration is 3 and the sum of the series is 160

Mathematics
1 answer:
Marina CMI [18]2 years ago
3 0
\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=4\\
r=3\\
S_n=160
\end{cases}

\bf 160=4\left( \cfrac{1-3^n}{1-3} \right)\implies 160=4\left( \cfrac{1-3^n}{-2} \right)\implies 160=-2(1-3^n)
\\\\\\
160=2(3^n-1)\implies \cfrac{160}{2}=3^n-1\implies 80=3^n-1
\\\\\\
81=3^n~~
\begin{cases}
81=3\cdot 3\cdot 3\cdot 3\\
\qquad 3^4
\end{cases}\implies 3^4=3^n\implies 4=n
You might be interested in
B. If there are players on the teams, how many stages will it take to notify all of the players? Show your work below.
Georgia [21]

Answer:

sir we need more context

Step-by-step explanation:

5 0
3 years ago
Match each quadratic equation with the best way to solve it.
Blizzard [7]

Answer:

5x^2 + 12x -3 =0 ---------> solve by quadratic formula

x^2 -4x = 8          ----------> solve by completing the square

4x^2 -25 = 0        ----------> solve by square root method

x^2-5x+ 6 = 0       -----------> solve by factoring

Step-by-step explanation:

1. 5x^2 + 12x -3 =0

The best way to solve this equation is quadratic formula as all the terms in the equation have coefficients it will be convenient to solve it through quadratic formula.

2. x^2 -4x = 8

The best way to solve this equation is by completing the square as the factors cannot be made directly.

3. 4x^2 -25 = 0

the best way to solve this equation is to solve by square root method as the 25 and 4 are perfect squares.

4. x^2-5x+ 6 = 0

The best way to solve this equation is to solve by factoring as it can clearly be seen that it is convenient to make factors ..

7 0
3 years ago
the city park department is planning to enclose a play aea. one side of the area will be against an existing building, so no fen
SVEN [57.7K]

Answer:

length = 200 m

width = 400 m

Step-by-step explanation:

Let the length of the plaing area is L and the width of the playing area is W.

Length of fencing around three sides = 2 L + W = 800

W = 800 - 2L ..... (1)

Let A is the area of playing area

A = L x W

A = L (800 - 2L)

A = 800 L - 2L²

Differentiate with respect to L.

dA/dL = 800 - 4 L

It is equal to zero for maxima and minima

800 - 4 L = 0

L = 200 m

W = 800 - 2 x 200 = 400 m

So, the area is maximum if the length is 200 m and the width is 400 m.

8 0
3 years ago
Read 2 more answers
The number of bacteria in a Petri dish increases by 18% every hour. If there were initially 200 bacteria placed in the Petri dis
In-s [12.5K]

Answer:

Step-by-step explanation:

an exponential equation has the form y=ar^x where y=final amount, a=initial amount, r=rate, and x=time, in this case

y=200(1.18)^x

5 0
3 years ago
Solve for k, 6k-2z=12
Alenkinab [10]
The previous question I answered was exactly like this.

6(4) - 2(6) = 12.

K = 4.
4 0
3 years ago
Other questions:
  • Help me please I really need help
    15·1 answer
  • Is Erik's statement correct? Why or why not?
    11·2 answers
  • What does n equal when -3 < n-8
    5·1 answer
  • Ellis took out a 20 year loan for $70,000 at an APR of 12.5% compounded monthly approximately what would be the total cost of hi
    9·2 answers
  • (HELP NEEDED) (PAST DUE) (STUCK) Please write a number line for the number 3
    7·2 answers
  • If f(x) = |-3x - 6| - 10, find f(5)
    11·2 answers
  • A house that is 30 feet tall casts a shadow that is 50 feet long. A nearby tree casts a shadow that is 75 feet long. HOW LONG IS
    13·1 answer
  • X:x is a square number and 20<x <100​
    8·1 answer
  • Find the perimeter of ABHG
    12·1 answer
  • Can i have help with this question please i don’t understand
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!