6 Questions
What is the common difference in an arithmetic progression?
The constant difference between consecutive terms
What is the formula to find the nth term of an arithmetic progression?
an = a1 + (n - 1)d
What is the formula to find the sum of the first 'n' terms of an arithmetic progression?
Sn = (n/2) × (a1 + an)
When the number of terms is even, how can the sum of an arithmetic progression be found?
By taking the average of the first and last terms and multiplying by the number of terms
What is the middle term added to when the number of terms in an arithmetic progression is odd?
The average of the first and last terms
What does the symbol 'd' represent in an arithmetic progression?
The common difference
Study Notes
Arithmetic Progression
Common Difference (d)
- The common difference is the constant difference between consecutive terms in an arithmetic progression.
- It is denoted by the symbol 'd'.
- d = a2 - a1 = a3 - a2 = ... = an - an-1, where 'a' represents the terms in the AP.
Nth Term (an)
- The nth term of an arithmetic progression can be found using the formula: an = a1 + (n - 1)d, where 'a1' is the first term and 'n' is the term number.
- This formula allows us to find any term in the progression.
Sum of Terms (Sn)
- The sum of the first 'n' terms of an arithmetic progression can be found using the formula: Sn = (n/2) × (a1 + an), where 'a1' is the first term and 'an' is the last term.
- This formula can be used to find the sum of any number of terms in the progression.
- When the number of terms is even, the sum can be found by taking the average of the first and last terms and multiplying by the number of terms.
- When the number of terms is odd, the sum can be found by taking the average of the first and last terms, multiplying by the number of terms, and adding the middle term.
Arithmetic Progression
Common Difference (d)
- d is the constant difference between consecutive terms in an AP
- d is denoted by the symbol 'd'
- d = a2 - a1 = a3 - a2 = ... = an - an-1, where 'a' represents the terms in the AP
Nth Term (an)
- The nth term of an AP can be found using the formula: an = a1 + (n - 1)d
- a1 is the first term and 'n' is the term number
- This formula allows us to find any term in the progression
Sum of Terms (Sn)
- The sum of the first 'n' terms of an AP can be found using the formula: Sn = (n/2) × (a1 + an)
- a1 is the first term and 'an' is the last term
- When the number of terms is even, the sum can be found by taking the average of the first and last terms and multiplying by the number of terms
- When the number of terms is odd, the sum can be found by taking the average of the first and last terms, multiplying by the number of terms, and adding the middle term
Learn about the common difference and nth term of an arithmetic progression, including formulas and definitions.
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