Question
Write an expression for the nth term in the sequence 3, 5, 7, 9, 11, … and find the value of the 100th term.
- 201
- 200
- 202
- 199
Hint:
The terms are all odd numbers. - First look similarities and differences between the terms.
Each term is greater than the one before it.
The difference between one term and the next one is 2.
Assume that each term is going to be 2 more than the one before it. (They will all continue to be odd) - Generalize the observations.
The next terms will be 13, 15, and 17.
Terms 1 is 3.
Terms 2 is 5.
Terms 3 is 7.
Term 4 is 9. - Write a conjecture. Since the problem asks for the nth term, we want an algebraic expression that connects the position of the term in the sequence to the term's value.
As the term position goes up by 1, the term value goes up by 2.
Try multiplying the term position by2:
Term 1 gives 2.
Term 2 gives 4.
Term 3 gives 6.
Each of these is too low by 1, so add 1:
Term 4 is 2 × 4 + 1 = 9. That worked!
The nth term has value 2n + 1. - Make the prediction requested by the problem. (This step may not always be needed.)
The 100th term has a value of 2(100) + 1, or 201.
The nth term is 2n + 1, and the 100th term is 201.
The correct answer is: 201
We were given with a pattern and asked to find the nth term general equation and also find the 100th term
While solving the question we observed how the pattern is changing for different value of n. and then obtained the general equation.
Related Questions to study
Look at the pattern: 3, 6, 12, 24, 48, ...
Make a rule for the nth term.
We obsrved the pattern with a table how it changed for different value of n. From the table we derived the general equation.
Look at the pattern: 3, 6, 12, 24, 48, ...
Make a rule for the nth term.
We obsrved the pattern with a table how it changed for different value of n. From the table we derived the general equation.
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.
