8
CBSE Marks
★★★★★
Difficulty
9
Topics
High
Board Weight
Topics Covered
9 key topics in this chapter
What is an AP?
Common Difference
nth Term Formula aₙ = a+(n−1)d
Finding Number of Terms
Sum of First n Terms
Sum Formula: Sₙ = n/2·[2a+(n−1)d]
Sum when Last Term is Known
Arithmetic Mean
Word Problems
Study Resources
Key Formulas
| Formula / Rule | Expression |
|---|---|
| nth Term | \(aₙ = a + (n−1)d\) |
| Sum of n Terms | \(Sₙ = n/2·[2a + (n−1)d]\) |
| Sum (last term) | \(Sₙ = n/2·(a + l)\) |
| Arithmetic Mean | \(AM = (a + b)/2\) |
| nth Term from End | \(aₙ = l − (n−1)d\) |
Important Points to Remember
The common difference d = aₙ − aₙ₋₁ is constant throughout an AP.
The nth term from the end of an AP = l − (n−1)d, where l is the last term.
If three numbers are in AP: take them as a−d, a, a+d (sum = 3a).
If four numbers are in AP: take them as a−3d, a−d, a+d, a+3d.