

Divisibility and Mathematical Induction
Interactive Video
•
Mathematics
•
9th - 10th Grade
•
Practice Problem
•
Hard
Aiden Montgomery
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main condition for the number 3^n + 70n to be divisible by 10?
n must be an odd positive integer
n must be an even integer
n must be a positive integer
n must be a negative integer
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in mathematical induction?
Assume the statement is true for n=k
Test the statement for the first possible value of n
Find a counterexample
Prove the statement for n=k+1
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is n=1 chosen as the first value to test in this problem?
Because 1 is the smallest positive integer
Because 1 is the first odd number
Because 1 is an even number
Because 1 is a prime number
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a key property of odd numbers that is relevant to this proof?
Odd numbers are always greater than even numbers
Odd numbers are divisible by 2
Odd numbers are always prime
Odd numbers can be expressed as 2k+1
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What issue arises when using 2k-1 in the exponent?
It introduces fractions
It simplifies the calculation
It makes the expression even
It introduces negative exponents
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is it inefficient to use negative exponents in this proof?
They introduce fractions
They make the expression even
They simplify the calculation
They make the expression odd
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the benefit of using an equivalent version of an assumption?
It makes the proof longer
It introduces more variables
It simplifies the problem
It makes the proof more complex
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