Questions and Answers
What defines a term in an arithmetic progression (AP) after the first term?
Given the AP with the first term 1 and common difference 2, what is the 4th term?
Which of the following sequences is NOT an arithmetic progression?
What is the common difference of the arithmetic progression -4, -14, -24?
Signup and view all the answers
Which of the following statements about the sequence 5, 2, -1, -4, -4, -4 is correct?
Signup and view all the answers
What is the common difference in the arithmetic progression 5, 2, -1, -4, -4, -4, -4?
Signup and view all the answers
What is the 4th term of the sequence defined by $t_n = 3n + 5$?
Signup and view all the answers
Which of the following sequences is NOT an arithmetic progression?
Signup and view all the answers
What is the formula for the n-th term of the sequence where the first term is 8?
Signup and view all the answers
How many terms does the sequence 1, 1, 2, 3, 5 contain before it is no longer an arithmetic progression?
Signup and view all the answers
What is the common difference in the arithmetic progression 5, 2, -1, -4, -4, -4,...?
Signup and view all the answers
What is the 4th term of the sequence defined by the formula $t_n = 3n + 5$?
Signup and view all the answers
Study Notes
Arithmetic Progression (AP)
- A sequence where every term beyond the first is derived by adding a constant known as the common difference.
- Common difference can be positive, negative, or zero, affecting the sequence's direction.
Examples of Arithmetic Progressions
- Example 1: 3 — AP with first term 1 and common difference 2.
- Example 2: -4, -14 — AP with first term 6 and common difference -10.
- Example 3: 1, 1, 2, 3, 5 — Example of an AP, not strictly linear.
- Example 4: 5, 2, -1, -4, -4, -4 — Another AP showcasing repeated terms.
Formula for the nth Term
- The nth term of an AP can be expressed using the formula: [ t_n = 3n + 5 ]
- Where n represents the term number starting from 1.
Calculation of the First Five Terms
-
1st Term:
- ( t_1 = 3 \times 1 + 5 = 8 )
-
2nd Term:
- ( t_2 = 3 \times 2 + 5 = 11 )
-
3rd Term:
- ( t_3 = 3 \times 3 + 5 = 14 )
-
4th Term:
- ( t_4 = 3 \times 4 + 5 = 17 )
-
5th Term:
- ( t_5 = 3 \times 5 + 5 = 20 )
Summary of Key Points
- Arithmetic Progressions are characterized by a constant difference between consecutive terms.
- The common difference thoroughly defines the progression's structure.
- Identifying the nth term formula is crucial for calculating specific terms within the sequence.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of arithmetic progressions with this quiz. Explore the concept of the common difference and how it relates to the terms in a sequence. Ideal for students learning about sequences in mathematics.
