Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.3 + 8 + 13 + ... + (5n - 2) = 
(5n + 1)
What will be an ideal response?
First we show that the statement is true when n = 1.
For n = 1, we get 3 = 
(5(1) + 1) = 3.
This is a true statement and Condition I is satisfied.
Next, we assume the statement holds for some k. That is,
is true for some positive integer k.
We need to show that the statement holds for k + 1. That is, we need to show that
So we assume that 
is true and add the next term, 
, to both sides of the equation.
3 + 8 + 13 + ... + (5k - 2) + 5(k + 1) - 2 = 
(5k + 1) + 5(k + 1) - 2
= 
[k(5k + 1) + 10(k + 1) - 4]
= 
(5k2 + k + 10k + 10 - 4)
= 
(5k2 + 11k + 6)
= 
(k + 1)(5k + 6)
= 
(5k + 5 + 1)
= 
(5(k + 1) + 1)
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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Graph the numbers on the real number line.x < -6
A. 
B. 
C. 
D. 
The perpendicular bisectors of two chords of a circle intersect at the center of the circle if ______________________
What will be an ideal response?
Solve the problem.The second angle of a triangle is 3 times as large as the first. The third angle is 70° more than the first. Find the measure of the smallest angle.
A. 110° B. 70° C. 22° D. 20°
A manufacturing company wants to maximize profits on products A, B, and C. The profit margin is $3 for A, $6 for B, and $15 for C. The production requirements and departmental capacities are as follows: 
What are the constants in the model?
A. 30,000, 38,000, 28,000 B. 2, 3, 3 C. 3, 6, 15 D. 1, 2, 2