Sum of n terms of AP formula: Sₙ = n/2 [2a + (n − 1)d]
The sum of n terms of AP formula is Sₙ = n/2 [2a + (n − 1)d] = n/2 (a + l).
What each letter means
- \(S_n\) the sum of the first n terms of the AP
- \(a\) the first term
- \(d\) the common difference
- \(l\) the last term
- \(n\) the number of terms
When to use it
To add up the first n terms of an arithmetic sequence. Use the second form when you know the last term.
Worked example
Find the sum of the first 20 terms of the AP \(2, 7, 12, \dots\)
- \(a=2,\ d=5,\ n=20\)
- \(S_{20}=\dfrac{20}{2}\big[4+19\times5\big]=10\times99\)
Answer: \(S_{20}=990\)
Common mistake
Halving only one part. The whole bracket is multiplied by n/2.
On your course
| Course | In the exam |
|---|---|
| Class 10 | Learn it: CBSE gives no formula booklet |
From our own CBSE Maths formula sheets, in our words.
Practise and revise
![Sum of n terms of an AP formula card: Sₙ = n/2 [2a + (n − 1)d] = n/2 (a + l). CBSE Math Revision](/cbse-frontend/img/formula-cards/cbse-maths-sum-of-arithmetic-series-formula-card.png)
Questions
What is the sum of n terms of AP formula?
The sum of n terms of AP formula is Sₙ = n/2 [2a + (n − 1)d] = n/2 (a + l). Sₙ: the sum of the first n terms of the AP; a: the first term; d: the common difference; l: the last term; n: the number of terms.
Is the sum of n terms of an AP given in the exam?
Class 10: learn it: CBSE gives no formula booklet. This comes from our own CBSE Maths formula sheets; your teacher has the official booklet.
What is the difference between a sequence and a series?
A sequence is a list of terms. A series is what you get when you add the terms, so Sₙ is the sum of the first n terms.
Our own wording, examples and card, checked by CBSE Math Revision. Not produced or endorsed by CBSE or NCERT.