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
MArishka [77]
3 years ago
15

the common ratio of a geometric series is 3 and the sum of the first 8 terms is 3280. what is the first term of the series?

Mathematics
1 answer:
andrew11 [14]3 years ago
4 0

Answer: 1

Step-by-step explanation:

The formula for calculating the sum of a Geometric series if the common ratio is greater than 1 is given as :

S_{n} = \frac{a(r^{n}-1) }{r-1}

Where S_{n} is the sum of terms , a is the first term , r is the common ratio and n is the number of terms.

From the question:

S_{n} = 3280

a = ?

r = 3

n = 8

Substituting this into the formula , we have

3280 = \frac{a(3^{8}-1) }{3-1}

3280 = \frac{a(6561-1)}{2}

Multiply through by 2 , we have

6560 = a ( 6560)

divide through by 6560, we have

6560/6560 = a(6560)/6560

Therefore : a = 1

The first term of the series is thus 1

You might be interested in
The sum of four times a number and five times another number is -28. The sum of nine times the first number and two times the se
dedylja [7]

Answer:

  -8

Step-by-step explanation:

If we let x and y represent the first and second numbers, respectively, we can write the problem statement as the equations ...

  • 4x +5y = -28
  • 9x +2y = 11

We can multiply the first equation by -9 and add 4 times the second equation to get an equation in y alone:

  -9(4x +5y) +4(9x +2y) = -9(-28) +4(11)

  -37y = 296 . . . . . simplify

  296/-37 = y = -8 . . . . . divide by the coefficient of y

The second number is -8.

7 0
3 years ago
Simplify each exponential expression using the properties of exponents and match it to the correct answer.
saveliy_v [14]

1) (2\times3^-2)^3 (5\times3^2)^2 / (3^-2)(5\times2)^2 = 2

2) (3^3) (4^0)^2 (3\times2)^-3 (2^2) = 1/2

3) (3^7\times4^7) (2\times5)^-3 (5)^2 / (12^7) (5^-1) (2^-4) = 2

4) (2.3)^-1 (2^0) / (2.3)^-1 = 1

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

Step 1 :

(2\times3^-2)^3 (5\times3^2)^2 / (3^-2)(5\times2)^2

⇒ (2^3) (3^-6) (5^2) (3^4) / (3^-2) (10^2)

⇒ (2.2^2.5^2) (3^-6.3^4) / (3^-2) (10^2)

⇒ (2)(10^2) (3^-2) / (3^-2) (10^2)

⇒ 2

Step 2 :

(3^3) (4^0)^2 (3\times2)^-3 (2^2)

Any number with power 'zero' is 1.

⇒ (3^3) (1^2) (3^-3) (2^-3) (2^2)

⇒ (2^(-3+2))

⇒ 2^-1 = 1/2

Step 3 :

(3^7\times4^7) (2\times5)^-3 (5)^2 / (12^7) (5^-1) (2^-4)

⇒ (12^7) (2^-3) (5^-3) (5^2) / (12^7) (5^-1) (2^-4)

⇒ (12^7) (2^-3) (5^-3) (5^2) / (12^7) (5^-1) (2^-4)

⇒ (2^-3) (5^(-3+2)) / (5^-1) (2^-4)

⇒ (2^-3) (5^-1) / (5^-1) (2^-4)

⇒ 1 / (2^-1)

⇒ 2

Step 4 :

(2.3)^-1 (2^0) / (2.3)^-1

⇒ (2^0)

⇒ Any number with power 'zero' is 1

⇒ 1

8 0
3 years ago
The question is in the image! Please help if u can its due really soon
maw [93]

Answer:

5.4

Step-by-step explanation:

3x+38=10x

-3x         -3x

38=7x

x=5.4

Brainliest pleaseeeeeee

7 0
3 years ago
Read 2 more answers
What is an equation that models the sequence 400, 200, 100, 50, ?
katrin [286]
N / 2

400 / 2 = 200
200 / 2 = 100
100 / 2 = 50
50 / 2 = 25
25 / 2 = 12.5
4 0
3 years ago
Solve. −425=x−114 What is the solution to the equation? Enter your answer as a simplified mixed number in the box. FIRST PERSON
Maksim231197 [3]

Answer:

-311

Step-by-step explanation:

−425 = x − 114

=> x = -425 + 114

=> x = -311

Therefore, -311 is our answer.

Hoped this helped.

8 0
3 years ago
Other questions:
  • Which one of the following letters would be considered formal?
    9·1 answer
  • What is the area of the polygon??
    8·1 answer
  • A sanitation department is interested in estimating the mean amount of garbage per bin for all bins in the city. Assume the amou
    11·1 answer
  • Actually can ride her bike 15 miles in two hours there are 60 minutes in one hour and there are 1760 yards in 1 mile how many ya
    6·1 answer
  • Miriam ha a bag that contain 10 red marbles and 6 blue marbles . she chooses two marbles at random and does not replace them. Wh
    10·1 answer
  • If a • b = b, what must the value of a be?
    10·1 answer
  • 3=e/2 what is e then?
    9·1 answer
  • 1) Change the base of the function y= 4 × 8^x to base 2. options:
    12·1 answer
  • The Johnson family want to start a college fund for their daughter Gabriella. They put $63, 000 in to an account that grows at a
    15·1 answer
  • HELLLLLLP RNNN PLSSSSSSSSSSSS
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!