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
4vir4ik [10]
3 years ago
13

Find the sum of the first fifteen terms of the series:

Mathematics
1 answer:
bija089 [108]3 years ago
4 0

Answer:

Step-by-step explanation:

The given series is a geometric series because the consecutive terms differ by a common ratio. The formula for determining the sum of the first n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1)/(r - 1)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

a = 3

r = 6/3 = 12/6 = 2

n = 15

Therefore, the sum of the first 15 terms, S15 is

S15 = (3 × 2^(15) - 1)/2 - 1

S15 = (3 × 32767)/1

S15 = 98301

You might be interested in
5(x+4)= -2(-4-x)+3 <br> what is the answer?
lianna [129]

Answer:

x = -3

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

5(x + 4) = -2(-4 - x) + 3

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute:                                   5x + 20 = 8 + 2x + 3
  2. Combine like terms:                   5x + 20 = 2x + 11
  3. Subtract 2x on both sides:        3x + 20 = 11
  4. Subtract 20 on both sides:        3x = -9
  5. Divide 3 on both sides:              x = -3

<u>Step 3: Check</u>

<em>Plug in x to verify it's a solution.</em>

  1. Substitute:                    5(-3 + 4) = -2(-4 - -3) + 3
  2. Simplify:                        5(-3 + 4) = -2(-4 + 3) + 3
  3. Add:                              5(1) = -2(-1) + 3
  4. Multiply:                        5 = 2 + 3
  5. Add:                              5 = 5

Here we see that 5 does indeed equal 5. ∴ x = -3 is a solution of the equation.

And we have our final answer!

5 0
3 years ago
Read 2 more answers
(100 points) Give a step by step explanation on how you solved this problem
Lina20 [59]
Use substitution
Given both y values, you know that they have to be equal

3x + 3 = x - 1
2x + 3 = -1
2x = -4, divide by 2
x = -2
Now plug x value into any of the equation to find y value
y = 3(-2) + 3
y = -6 + 3, y = -3

Solution: x = -2, y = -3
4 0
3 years ago
Read 2 more answers
Click on the graphic to select the figure that would make the following "a reflection in line k.
Reil [10]

there seem to be pictures missing. can you reload the page without losing progress?

5 0
3 years ago
A person standing on a moving walkway travels 75 feet in 25 seconds. What equation represents this relationship? How many feet w
Goryan [66]

Answer: B

Step-by-step explanation: divide 75 by 25 to find how many feet you travel in 1 second (75/25=3) then you take 3 times 10 to see how many feet you travel in 10 seconds (3x10=30).

3 0
3 years ago
A scientist measured the water pressure at different depths. She made a table showing her findings. The x-values represent the d
inessss [21]

Answer:

100,70 is the answer I took the test

5 0
3 years ago
Other questions:
  • The length of a rectangle is 4 feet more than the width. If the perimeter is 20 ft. What is the length of the rectangle?
    12·1 answer
  • in a quadrilateral, two of the angles each have a measure of 40°, and the measure of a third angle is 130°. What is the measure
    13·1 answer
  • In parallelogram LMNO, what are the values of x and y?
    14·2 answers
  • Combine like terms 7a - a+ 16 = ?
    8·2 answers
  • If A and B represent integers, M+P = P+M is an example of which property?
    15·2 answers
  • Write an equation in slope intercept form with a slope of 1/4 and a y-intercept of 6
    10·1 answer
  • Add the following using horizontal method<br><br>i.)abc,-2abc,4abc<br><br>ii.)8xz,-2xz,-6xz
    13·2 answers
  • The U-Pick-It Farm wants to find out which type of berries their customers
    9·1 answer
  • Please help me, I forgot how to do this
    6·1 answer
  • A box contains 14 large marbles and 10 small marbles. Each marble is either green or white 8 of the large marbles are green, and
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!