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Questions and Answers
What is the common difference of an arithmetic progression?
What is the common difference of an arithmetic progression?
What is the formula for the nth term of an arithmetic progression?
What is the formula for the nth term of an arithmetic progression?
What is the formula for the sum of the first 'n' terms of an arithmetic progression?
What is the formula for the sum of the first 'n' terms of an arithmetic progression?
What is the symbol used to denote the common difference of an arithmetic progression?
What is the symbol used to denote the common difference of an arithmetic progression?
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What is the term used to describe the nth term of an arithmetic progression?
What is the term used to describe the nth term of an arithmetic progression?
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Study Notes
Arithmetic Progression
Common Difference (d)
- The common difference is the difference between any two consecutive terms in an arithmetic progression.
- It is denoted by the symbol 'd'.
- The common difference is constant for an arithmetic progression.
- Formula: d = an - an-1, where an is a term in the sequence and an-1 is the preceding term.
Nth Term (an)
- The nth term of an arithmetic progression is given by the formula: an = a1 + (n-1)d
- Where:
- an is the nth term
- a1 is the first term
- n is the term number (starting from 1)
- d is the common difference
Sum of Terms (Sn)
- The sum of the first 'n' terms of an arithmetic progression is given by the formula: Sn = (n/2)(a1 + an)
- Where:
- Sn is the sum of the first 'n' terms
- a1 is the first term
- an is the nth term
- This formula is known as the formula for the sum of an arithmetic series.
Arithmetic Progression
Common Difference (d)
- Common difference (d) is the difference between any two consecutive terms in an arithmetic progression.
- The symbol 'd' denotes the common difference.
- The common difference is constant in an arithmetic progression.
- The formula to find the common difference is d = an - an-1, where an is a term in the sequence and an-1 is the preceding term.
Nth Term (an)
- The formula to find the nth term of an arithmetic progression is an = a1 + (n-1)d.
- In this formula, an is the nth term, a1 is the first term, n is the term number (starting from 1), and d is the common difference.
Sum of Terms (Sn)
- The formula to find the sum of the first 'n' terms of an arithmetic progression is Sn = (n/2)(a1 + an).
- In this formula, Sn is the sum of the first 'n' terms, a1 is the first term, and an is the nth term.
- This formula is known as the formula for the sum of an arithmetic series.
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Description
Learn about the common difference and nth term formulas in arithmetic progressions. Understand how to calculate them with the given formulas.
