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
Gnoma [55]
3 years ago
15

What is the first term in a geometric sequence if the common ratio is −3 and the sum of the first five terms is 427?

Mathematics
1 answer:
Marina86 [1]3 years ago
4 0
So, we know that r = -3, and that the sum of the first 5 terms is 427 hmmmm

\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}\\
----------\\
n=5\\
r=-3\\
S_5=427
\end{cases}
\\\\\\
S_5=a_1\left( \cfrac{1-r^5}{1-r} \right)\implies 427=a_1\left( \cfrac{1-(-3)^5}{1-(-3)} \right)

\bf 427=a_1\left(\cfrac{1+243}{1+3}  \right)\implies 427=a_1(61)\implies \cfrac{427}{61}=a_1\implies 7=a_1
\\\\\\
n^{th}\textit{ term of a geometric sequence}\\\\
a_n=a_1\cdot r^{n-1}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
r=-3\\
n=5\\
a_1=7
\end{cases}
\\\\\\
a_5=7 (-3)^{5-1}\implies a_5=7(-3)^4

and surely you know how much that is.<span />
You might be interested in
Four students simplified the expression.
Viktor [21]

Answer:

camilaaaaaaaaaaaaaaa

6 0
2 years ago
Read 2 more answers
The 8 foot diameter circular table has a 4 foot wide extension. What is the total area with the extension? How does the area com
Ann [662]
To compare the areas of the table without the extension and the table with the extension, you would need to find the areas of both. See the attached page for the area of the table with the extension. To compare this to a table with a diameter of 10 ft, you need to calculate the area of the table that has a diameter of 10 feet. See the attached page for this information as well. When you're done make a comparison statement giving both pieces of information in your answer.

3 0
3 years ago
#every one when im in public be like
Zina [86]

Answer:

lol

Step-by-step explanation:

8 0
2 years ago
The circle below has center k , and its radius is 3 cm Given that m∠LKM =70° , find the length of the major arcLNM
Veseljchak [2.6K]

The length of the major arc LNM is \frac{29}{6}\pi \ cm

<h3><u>Length of an arc</u></h3>

From the question,

We are to determine the value of the length of the major arc LNM

The length of the major arc LNM can be calculated using the formula

Length \ of \ major\ arc \ LNM = \frac{Reflex \

Where r is the radius

First, we will determine the value of the reflex ∠LKM

Reflex ∠LKM + ∠LKM = 360° (<em>Sum of angles at a point</em>)

From the given information,

∠LKM = 70°

Then,

Reflex ∠LKM + 70° = 360°

Reflex ∠LKM = 360° - 70°

Reflex ∠LKM = 290°

Also, from the question

r = 3 cm

Now, putting the parameters into the formula, we get

Length \ of \ major\ arc \ LNM = \frac{290 ^\circ }{360 ^\circ} \times 2\pi \times 3

Then,

Length \ of \ major\ arc \ LNM = \frac{1740\pi}{360}

Length \ of \ major\ arc \ LNM = \frac{29}{6} \pi \ cm

Hence, the length of the major arc LNM is \frac{29}{6}\pi \ cm

Learn more on calculating length of an arc here: brainly.com/question/2005046

5 0
2 years ago
What is the solution to the following system of equations?
liraira [26]

Answer:

x = 6 ,  y = -2

Step-by-step explanation:

2 x + 3 y = 6  (Equation 1)

x + y = 4        (Equation 2)

<u>Solving by substitution</u> :

(Equation 2) ⇒ y = 4 - x

<u>Substitute y by 4 - x in (equation 1)</u> :

2 x + 3 (4 - x) = 6

Then

2 x + 12 - 3x = 6

Then

12 - x = 6

Then

12 - 6 = x

Then

x = 6

<u>We obtain</u> :

y = 4 - x and x = 6

Then

y = 4 - 6

  = -2

6 0
1 year ago
Read 2 more answers
Other questions:
  • Forty percent of the players on a soccer team are experienced players. The coach wants to increase this percent. There are 10 pl
    15·1 answer
  • Two trains leave stations 216 miles apart at the same time and travel toward each other. one train travels at 85 miles per hour
    6·1 answer
  • Mr. Saenz earned $240 for working 3 eight hour shifts at the lumber yard. What's his hourly wage?
    10·1 answer
  • How many millimeters are in 20 meters ​
    14·2 answers
  • Plz Help!!!!!!!!!! 14. Teenagers should sleep between 8 and 10 hours per night. Sarah typically sleeps 2 hours less than this pe
    8·1 answer
  • Team rose over run canoed 15 3/4 miles in 2 1/4 hours what was their average rate of speed in miles per hour
    12·1 answer
  • 44.69 rounded to the nearest tenth
    7·1 answer
  • The RideEm Bicycles factory can produce 100 bicycles in a day at a total cost of $10,900, and it can produce 120 bicycles in a d
    11·1 answer
  • Question 14 *blue bubble*
    11·1 answer
  • rohana wants to find the volume of a sphere that has a radius of 10 feet. which equation can she use to solve for this value in
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!