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
Use the data in the table to write a multiplication or a division story for each number fact.Solve.
jolli1 [7]
10÷5=2 that is a division
4 0
3 years ago
Graph the ordered pairs for y = 4x + 2 <br> using {-2,1,2}
deff fn [24]
No clue there has to be a graph paper for the answer
3 0
3 years ago
3. Use the polynomial 12x^4 y^2 + 30x^3 y to answer the following questions?
barxatty [35]

Answer:

\huge\boxed{GCF:6x^3y}

\huge\boxed{Factored: 6x^3y(2x+5)}

Step-by-step explanation:

Look at both terms separately, and isolate each "part."

i.e. 12x^4y^2 becomes 12, x^4, y^2

So the problem becomes:

12, x^4, y^2 and

30, x^3, y^1

Then, find the GCF of each term,

30 and 12 - 6

x^4 and x^3 - x^3

y^2 and y^1 - y^1

Hope it helps :) and let me know if you want me to elaborate.

7 0
2 years ago
Lily quinn makes $12.50 and hour. she works four hours on monday, six hours on tuesday, nine hours on wednesday, three hours on
AnnZ [28]
The answer is A. Her gross pay is $362.50.
4 0
3 years ago
How many perfect cube divisors does 160,000 have?
olasank [31]

Answer:

40

Step-by-step explanation:

brain-list if correct pls :D

6 0
2 years ago
Other questions:
  • Natalie and Preston would like to accumulate $25,000 at the end of 3.5 years for a future down payment on a house in Prescott. H
    11·1 answer
  • What is the length (magnitude) of the vector (7,-2)?
    6·1 answer
  • Which of these is a formal definition in
    15·1 answer
  • A postcard has an area of 10 square inches. Two enlargements of the postcard have areas of 40 square inches and 160 square inche
    8·1 answer
  • If f(x) = x^2 is vertically stretched by a factor of 3 and shifted down 7 to form g(x), which of the following equations best re
    9·2 answers
  • Write each vector described below in component form and find its magnitude. Draw an arrow originating from (0,0) to
    6·1 answer
  • If you have your net worth and assets, how do you get your liabilities?
    15·1 answer
  • What is the length of the missing leg? If necessary, round to the nearest tenth.
    15·1 answer
  • Formula of amount when interest and principal is given<br>​
    8·1 answer
  • What time is 1 hour and 37 minutes before 3:10
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!