Question

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

Answer 1

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

Answer 2

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?