can you check my answers?
Find Pk + 1 if
Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1)
7 + 13 + 19 + …+[6(k - 1) + 1] + (6k + 1) + [6(k + 1) + 1]
8 + 14 + 20 + …+[7(k - 1) + 1] + (7k + 1)
7 + 13 + 19 + …+(6k + 1)
7 + 13 + 19 + ...+[6(k - 1) + 1] + (6k7 +1) + (6k + 2)
answer:D
What is the first step when writing a proof using mathematical induction?
Assume that formula is true for Pk.
Find Pk + 1.
Verify formula is true for P1.
Find the sum of the integers.
answer :c
Which of the following shows the correct first step to prove the following by mathematical induction?
3 + 11 + 19 + 27 + … + (8n - 5) = n(4n - 1)
3 + 11 + 19 + 27 + … + (8 • 1 - 5) = 1(4 • 1 - 1)
8 • 1 - 5 = 1(4 • 1 - 1)
3 + 11 + 19 + 27 + … + (8k - 5) = k(4k - 1)
3 + 11 + 19 + 27 + … + (8k - 5) + [8(k + 1) - 5] = (k + 1)[4(k + 1) - 1]
answer:d
Find the second difference for the sequence.
7, 6, 7, 10, 15, 22, ….
1
2
3
5
answer:a
Find first differences for the sequence in order from a1 to a5. Determine whether or not the series is quadratic or not.
-1, -3, -1, 5, 15
2, 2, 6, 10; not quadratic
2, 2, 6, 10; quadratic
-2, 2, 6, 10; not quadratic
-2, 2, 6, 10; quadratic
answer: d
Find a quadratic model for the sequence.
-4, -4, -3, -1, 2
________________________________________
y = 0.5x2 - 0.5x - 4
y = 0.5x2 - 1.5x - 3
y = 4.5x2 - 21.5x+21
y = -4.5x2 + 21.4x - 21
answer: b
Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1)
P(k+1) = Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) + (6(k+1) + 1
= Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) + (6k + 7)
"What is the first step when writing a proof using mathematical induction? "
Test to see if it is true for n = 1
as shown in C for
"Which of the following shows the correct first step to prove the following by mathematical induction? "
for 7, 6, 7, 10, 15, 22, ….
1st difference is -1 , 1 , 3 , 5 , 7...
2nd difference is 2, 2, 2, 2, ..
next one: d is correct
last one: b is correct
For question 1 Find Pk + 1 if
Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) there isnt an option for the answer Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) + (6k + 7) so I am confused as to which is the correct answer.
for question 3 Which of the following shows the correct first step to prove the following by mathematical induction?
3 + 11 + 19 + 27 + … + (8n - 5) = n(4n - 1)
3 + 11 + 19 + 27 + … + (8 • 1 - 5) = 1(4 • 1 - 1)
8 • 1 - 5 = 1(4 • 1 - 1)
3 + 11 + 19 + 27 + … + (8k - 5) = k(4k - 1)
3 + 11 + 19 + 27 + … + (8k - 5) + [8(k + 1) - 5] = (k + 1)[4(k + 1) - 1]
Is d the correcct answer?
Let's go through each question and check your answers:
1. Find Pk + 1 if Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1).
Your answer: D
Correct answer: D
2. What is the first step when writing a proof using mathematical induction?
Your answer: C
Correct answer: C
3. Which of the following shows the correct first step to prove the following by mathematical induction: 3 + 11 + 19 + 27 + ... + (8n - 5) = n(4n - 1)?
Your answer: D
Correct answer: D
4. Find the second difference for the sequence: 7, 6, 7, 10, 15, 22, ...
Your answer: A
Correct answer: A
5. Find first differences for the sequence in order from a1 to a5. Determine whether or not the series is quadratic or not: -1, -3, -1, 5, 15.
Your answer: D
Correct answer: D
6. Find a quadratic model for the sequence: -4, -4, -3, -1, 2.
Your answer: B
Correct answer: B
Well done! Your answers are correct for all the questions. If you have any more questions or need further explanations, feel free to ask!