Arithmetic Progressions (NCERT Ch. 5)

• Identify an Arithmetic Progression (AP) — a sequence with a constant difference between consecutive terms.
• Find the nth term and the sum of n terms of an AP.

1. In an AP, the common difference (d) = any term minus the previous term; it is constant throughout.
2. nth term formula: aₙ = a + (n-1)d, where a is the first term.
3. Sum of n terms: Sₙ = (n/2)[2a + (n-1)d], or equivalently Sₙ = (n/2)(a + l) where l is the last term.

Find the 10th term of the AP: 3, 7, 11, 15, ...

a = 3, d = 7-3 = 4
a10 = a + (10-1)d = 3 + 9(4) = 3 + 36 = 39

• Using (n) instead of (n-1) in the nth term formula.
• Forgetting the common difference must be checked between ALL consecutive pairs, not just the first two.
• Sign errors when the AP is decreasing (negative common difference).

• Find the common difference of: 20, 15, 10, 5, ...
• Find the sum of the first 10 terms of the AP: 2, 4, 6, 8, ...

Open the Practice tab for graded questions on Arithmetic Progressions (NCERT Ch. 5).