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
Sphinxa [80]
3 years ago
8

Proof by mathematical induction

Mathematics
1 answer:
Ghella [55]3 years ago
5 0

Answer:

See below.

Step-by-step explanation:

I will assume that 3n is the last term.

First let  n = k, then:

Sum ( k terms) =  7k^2 + 3k

Now, the sum of k+1 terms  = 7k^2 + 3k + (k+1) th term

=  7k^2 + 3k + 14(k + 1) - 4

=   7k^2 + 17k + 10

Now 7(k + 1)^2 = 7k^2 +14 k + 7 so

7k^2 + 17k + 10

=  7(k + 1)^2  + 3k  + 3

= 7(k + 1)^2 + 3(k + 1)

Which is the  formula for the Sum of k terms with the k replaced by k + 1.

Therefore we can say if the sum formula is true for k terms then it is also true for (k + 1) terms.

But the formula is true for 1 term because  7(1)^2 + 3(1) = 10 .

So it must also be true for all subsequent( 2,3 etc) terms.

This completes the proof.

You might be interested in
Please jawab kakak ​
sertanlavr [38]
Sorry im not sure i understand the language your stating soo sorry
7 0
2 years ago
Pls help is it A. B. C. D.
Ivenika [448]

Answer:

C

Step-by-step explanation:

Hope I was able to help!! :)

7 0
3 years ago
the two lines represent the amount of water, over time, in two tanks that are the same size. Which container is filling more qui
uranmaximum [27]

The missing figure is attached down

Answer:

Container A is filling more quickly

Step-by-step explanation:

<em>Let us explain the linear relation</em>

The linear equation is y = m x + b, where

  • m is the slope of the line which represents the rate of change (change in y/change in x)
  • b is the y-intercept which means the initial amount of y (at x = 0)

<em>If a line represents the amount of water over time, then it represents the rate of filling of the water</em>

∵ There are two containers A and B that have the same size

∵ The two lines represent the amount of water over time in

    containers A and B

∴ The slopes of the lines represent the rat of water in the tanks

→ That means the greater slope represents the greater rate

∵ The greater the slope, the steeper the line

∴ The container that represented by the steeper the line is filling quickly

→ The line represents container A is steeper more than the line

    represents container B

∴ Container A is filling more quickly

4 0
3 years ago
A comparative box plot is shown for two data sets. Which statement is true? (Please help me and please if you're not 100% sure)
Elza [17]

Answer:

a

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
LONG WORD PROBLEM I KNOW! PLEASE ILL GIVE THANKS BRAINLIEST AND POINTS FOR THIS ANSWER! PLEASE!
11Alexandr11 [23.1K]
Answer:
5X + 8Y >= 300; intersection at (-20, 50)
Step-by-step explanation:
let t = work hours
0 < t < 30
X = time lawn mowing
Y = time babysitting.
X + Y < 30
5X + 8Y >= 300
We could solve...
X < 30 - Y
5(30 - Y) + 8Y >=300
150 - 5Y + 8Y >= 300
3Y >=150
Y >=50
then X < -20
intersection at (-20, 50)
5 0
3 years ago
Other questions:
  • Kelly decides to pour her punch into 1 quart containers to fit into her refrigerator until the party starts.she has four 1 quart
    15·1 answer
  • PLZZ HELP
    11·2 answers
  • A scale of a room in a blueprint is 3 in.:5 ft. A wall in the same blueprint is 18 in.
    11·1 answer
  • What is the length of ef and the measure of d?
    13·1 answer
  • Penelope determined the solutions of the quadratic function by completing the square.
    5·1 answer
  • The graph of y= x3 is transformed as shown in the graph below. Which equation represents the transformed function?
    8·2 answers
  • In the month of May, Blue Spruce Corp. Wrote checks in the amount of $75100. In June, checks in the amount of $102783 were writt
    7·1 answer
  • During a Team scavenger hunt event, the average number of steps taken was 1800. Calculate the distance traveled using 10,000 ste
    13·1 answer
  • A square and a rectangle have the same area. If the dimensions of the rectangle are 4 ft by 16 ft, how long is a side of the squ
    9·1 answer
  • when you first move into your current house, you noticed that a tree outside had a height of 63 inches. You noticed that after 3
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!