What is the formula for sum of n terms of an AP?

The sum of the first n terms of an AP is: Sₙ = n/2 × [2a + (n−1)d], where a = first term, d = common difference, n = number of terms. If the last term (l) is known, use: Sₙ = n/2 × [a + l].

How to find the nth term of an AP?

The nth term (general term) of an AP is: aₙ = a + (n−1)d, where a = first term, d = common difference, n = term position. Also, the nth term can be found from sums: aₙ = Sₙ − Sₙ₋₁.

What is the sum of first n natural numbers?

The sum of first n natural numbers (1 + 2 + 3 + ... + n) is n(n+1)/2. This is a special case of the AP sum formula with a = 1, d = 1. For example, sum of first 100 natural numbers = 100 × 101 / 2 = 5050.

Sum of AP Formula

Arithmetic Progressions • Class 10 Mathematics • NCERT • CBSE

The sum of the first n terms of an Arithmetic Progression is: Sn = n/2 × [2a + (n−1)d], where a is the first term and d is the common difference. Alternatively, if the last term l is known: Sn = n/2 × [a + l].

Key Formulas

aₙ = a + (n−1)d (nth term of AP)
Sₙ = n/2 × [2a + (n−1)d] (Sum of n terms)
Sₙ = n/2 × [a + l] (Sum when last term l is known)
aₙ = Sₙ − Sₙ₋₁ (nth term from sums)
Sum of first n natural numbers = n(n+1)/2

Frequently Asked Questions

What is the formula for sum of n terms of an AP?: The sum of the first n terms of an AP is: Sₙ = n/2 × [2a + (n−1)d], where a = first term, d = common difference, n = number of terms. If the last term (l) is known, use: Sₙ = n/2 × [a + l].
How to find the nth term of an AP?: The nth term (general term) of an AP is: aₙ = a + (n−1)d, where a = first term, d = common difference, n = term position. Also, the nth term can be found from sums: aₙ = Sₙ − Sₙ₋₁.
What is the sum of first n natural numbers?: The sum of first n natural numbers (1 + 2 + 3 + ... + n) is n(n+1)/2. This is a special case of the AP sum formula with a = 1, d = 1. For example, sum of first 100 natural numbers = 100 × 101 / 2 = 5050.

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