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
maxonik [38]
3 years ago
15

The sum of the first 3 terms of a geometric series is 171 and the common ratio is 2/3. What is the first term?​

Mathematics
2 answers:
goblinko [34]3 years ago
6 0

Answer:

81

Step-by-step explanation:

let the terms be a,ar,ar²

r=2/3

a+a(2/3)+a(2/3)²=171

multiply by 9

9a+6a+4a=171×9

19 a=171×9

a=(171×9)/(19)

a=9×9=81

alex41 [277]3 years ago
3 0

Answer:

The first term is 81

Step-by-step explanation:

The common ratio is 2/3.

r = \frac{2}{3}

Sum of first n terms in GP = S_n=\frac{a(1-r^n)}{1-r}

The sum of the first 3 terms of a geometric series is 171

n=3

Substitute the values in the formula:

S_3=\frac{a(1-(\frac{2}{3})^3}{1-\frac{2}{3}}

171=\frac{a(1-(\frac{2}{3})^3)}{1-\frac{2}{3}}

171(1-\frac{2}{3})=a(1-(\frac{2}{3})^3)

\frac{171(1-\frac{2}{3})}{(1-(\frac{2}{3})^3)}=a

81=a

Hence The first term is 81

You might be interested in
The coordinate plane below represents a city. Points A through F are schools in the city.
Usimov [2.4K]
Part A. The technique on how to find the equation that only applies to point D and E, is to create a line or curve that only includes two of these points. In this case, I created a random parabola that isolates points C and F from the rest of the points. First, we have to find the equation of the parabola through its general forms:

(x - h)² = +/-4a(y-k)      or    (y - k)² = +/-4a(x - h)

For parabolas drawn like that in the picture, the general form is (x - h)² = +4a(y-k), where the vertex is (h,k) and a is the distance from the vertex to the focus. From the picture, the vertex is at (0,3). Then, we use point D(-2,4) to determine a:

(-2 - 0)² = +4a(4 - 3)
4a = 4

So, the equation of the parabola is:

x² = 4(y - 3)
x² = 4y - 12

Part B. Point D was already verified above. Now for point E(2,4)
x² = 4y - 12
2² ? 4(4) - 12
4 ? 4
4 = 4

Part C. For y < 7x − 4, ignore the equality symbol first and graph the line. Assign random values of x, then you get corresponding values of y. Plot them as shown in the second picture. The line is shown in red. Next, test the equation by choosing a random point. Let's choose the purple point at (4,3).

3 ? 7(4) − 4
3 ? 24
3 < 24

Thus, it applies to the purple point, and all the other areas to that area. The shaded region are all solutions of the inequality. So, Erica is only interested in points E, C and F. 

5 0
3 years ago
Name a pair of alternate interior angles in the diagram. <br> -a.<br> -b.<br> -c.<br> -d.
FrozenT [24]

Answer:

c

Step-by-step explanation:

the answer is c

alernate angles are angles that take the shape of z

8 0
3 years ago
Help I will thank you
DENIUS [597]
The answer to the problem is 12. 2 times 3 is 6. 18 divided by 6 is 3 and 3 times 4 is 12.
8 0
3 years ago
Read 2 more answers
Approximately 32,200 citizens of a country died in automobile accidents in 2012. Express this toll in deaths per day.
Sunny_sXe [5.5K]
There are 365 days in a year. In the question, 32,200 people in one year. 32,200/365= Your answer of the approximate deaths in a day. 
4 0
3 years ago
The table shows the relationship of how many pounds of cherries are needed to make a certain number of pies:
posledela

Answer:

C. A graph is drawn. The horizontal axis and vertical axis values are 0 to 70 in increments of 10. The horizontal axis label is Number of Pies, and the vertical axis label is Pounds of Cherries. Points are plotted on the ordered pairs 30, 20 and 45, 30 and 60, 40.

Step-by-step explanation:

If we take two of the original points from the data and put them in to two point form we get the following equation.

(6,4) and (12,8)

(y-4) = [(8-4)/(12-6)](x-6)

y = 2/3x

You have to start a the origin since we can only have enough ingredients to make pies and we can't start with partial pies. So move to y intercept up by 2.

Put the x values in for answer C and you'll return the y values.

6 0
3 years ago
Other questions:
  • what number should be added to the expression x squared+2x to change it into a perfect square trinomial?
    14·2 answers
  • What are the 2 inequality?
    14·1 answer
  • An amoeba is an organism with one cell. A picture of an amoeba is drawn to the scale of 250:1. The amoeba in the picture is 9cm
    8·1 answer
  • 4. Assume that you have a part-time job at which you work 20 hours per week at the rate
    5·1 answer
  • Which product is negative?
    9·1 answer
  • Please help will mark you brainliest. ( all links will be reported)
    12·2 answers
  • At what angle is the cyclist riding on the steep road?
    14·1 answer
  • The table shows the average chick weight in grams of sixteen different species of birds.
    8·1 answer
  • *PLEASE HELP* *SPAM =REPORTED* 100 POINTS * PLEASE ADD EXPLANATION
    13·1 answer
  • What is Rational Number​
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!