Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.5 + 5 ? 
+ 5 ? 
2 + ... + 5 ? 
n - 1 = 
What will be an ideal response?
First we show that the statement is true when n = 1.
For n = 1, we get 3 = 
= 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.
5 + 5 ? 
+ 5 ? 
2 + ... + 5 ? 
k - 1 + 5 ? 
(k + 1) - 1= 
+ 5 ? 
(k + 1) - 1
= 
+ 5
k
= 
+ 
= 
= 
= 
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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Solve the problem.Rule: The sum of any two horizontally adjacent numbers is the number immediately below them. Use this rule to complete the array. 
A. 
B. 
C. 
D. 
Find the value of the expression.
? 
A. 
B. 
C. 
D. 
Find the difference. Assume that all variable factors in the denominators are not equal to zero.
- 
A. 
B. 5
C. 
D. 
Write an equation for the line with an x-intercept of -4 and y-intercept of 16.
What will be an ideal response?