Question
Look at the pattern: 3, 6, 12, 24, 48, ...
Make a rule for the nth term.
- 3 × 2n-1
- 2n - 1
- 2n - 1
- 2n + 1
Hint:
The given pattern is 3,6,12,24,48
So lets observe how it changed for different value of n
Using this equation, the 10th term will be 3 × 29, or 1536. Notice that the exponent is one less than the term number. So, for the nth term, the equation would be 3 × 2n-1
The correct answer is: 3 × 2n-1
In the question we were asked to find the general equation of given pattern we can do that by observing the pattern carefully
We obsrved the pattern with a table how it changed for different value of n. From the table we derived the general equation.
Related Questions to study
Look at the pattern: 3, 6, 12, 24, 48, ...
What is the next term in the pattern?
In the solution first we found the general equation of the pattern and then found the next term = 96
Look at the pattern: 3, 6, 12, 24, 48, ...
What is the next term in the pattern?
In the solution first we found the general equation of the pattern and then found the next term = 96
Look at the pattern 2, 4, 6, 8, 10, ...
Describe the pattern and try and find an equation that works for every term in the pattern.
We observed number in each case and then obtained the general formula working for all the values of n.
General equation = 2n
Look at the pattern 2, 4, 6, 8, 10, ...
Describe the pattern and try and find an equation that works for every term in the pattern.
We observed number in each case and then obtained the general formula working for all the values of n.
General equation = 2n
Determine if this conjecture is true. If not, give a counterexample.
The difference between two negative numbers is a negative number.
Here we verified the above statement with a example. and proved that the statement is incorrect
Determine if this conjecture is true. If not, give a counterexample.
The difference between two negative numbers is a negative number.
Here we verified the above statement with a example. and proved that the statement is incorrect
If it is a number, then it is either positive or negative. What is an appropriate counterexample?
Here in this solution we understood definition of positive, negative. And found the counter example.
If it is a number, then it is either positive or negative. What is an appropriate counterexample?
Here in this solution we understood definition of positive, negative. And found the counter example.
If it is an angle, then it is acute. What is an appropriate counterexample?
We understood thhe general definition of acute angle and then eliminated the incorrect option to obtain the correct option
If it is an angle, then it is acute. What is an appropriate counterexample?
We understood thhe general definition of acute angle and then eliminated the incorrect option to obtain the correct option
How many squares will be in the 5th figure?
We observed first four figures carefully and then obtained a relaton to find no of squares in 5th figure = 70
How many squares will be in the 5th figure?
We observed first four figures carefully and then obtained a relaton to find no of squares in 5th figure = 70
Find the pattern to solve the sequence 2, 4, 7, 11….
So from the above solution we can say that +2,+3,+4... is the correct option
Find the pattern to solve the sequence 2, 4, 7, 11….
So from the above solution we can say that +2,+3,+4... is the correct option
Which is a counterexample of any number divisible by 2 is divisible by 4.
We eliminated the incorrrect options to obtain the correct option
Which is a counterexample of any number divisible by 2 is divisible by 4.
We eliminated the incorrrect options to obtain the correct option
Find the next item in the pattern:
- 3, 6, - 12, 24, ...
Here we observed the pattern in each stage and obtained a certain result to find the next erm
Find the next item in the pattern:
- 3, 6, - 12, 24, ...
Here we observed the pattern in each stage and obtained a certain result to find the next erm
Which of the following conjectures is false?
The false conjecture is the sum of two odd numbers id odd.
Which of the following conjectures is false?
The false conjecture is the sum of two odd numbers id odd.
A concluding statement reached using inductive reasoning is called a _______.
Therefore, the term used for a concluding statement reached using inductive reasoning is called conjecture.
A concluding statement reached using inductive reasoning is called a _______.
Therefore, the term used for a concluding statement reached using inductive reasoning is called conjecture.
Which of the following is the basis for inductive reasoning?
Therefore, observed patterns is the basis for inductive reasoning.
Which of the following is the basis for inductive reasoning?
Therefore, observed patterns is the basis for inductive reasoning.
Complete the conjecture.
The sum of two negative numbers is ___________.
Hence, the sum of two negative numbers is negative.
Complete the conjecture.
The sum of two negative numbers is ___________.
Hence, the sum of two negative numbers is negative.
Find a pattern in the sequence. Use the pattern to show the next two terms.
1, 3, 7, 15, 31, ___, ___
Therefore, the two numbers in the given sequence are 63 and 127
Find a pattern in the sequence. Use the pattern to show the next two terms.
1, 3, 7, 15, 31, ___, ___
Therefore, the two numbers in the given sequence are 63 and 127
