nth term of an AP
- CBSE · NCERT Class 10, Ch 5 Arithmetic Progressions
The nth term of an AP is its term in position n, given by aₙ = a + (n - 1)d.
Here a is the first term and d is the common difference. To reach the nth term, you start at a and add d a total of n - 1 times. Not n times: the first term already sits in position 1.
The formula works both ways. Given a position, it finds the value. Given a value, it finds the position. The last term of a finite AP is written l.
A small example
Which term of 20, 40, 60, ... is 380? Here a = 20 and d = 20.
- 380 = 20 + (n - 1) × 20
- 360 = (n - 1) × 20, so n - 1 = 18.
- n = 19. So 380 is the 19th term.
Where marks go
This AP comes from Question 28(B) of CBSE's 2026-27 Maths Standard sample paper. It asks for the sum of the integers between 1 and 400 that are multiples of both 4 and 5. Those are the multiples of 20, from 20 to 380.
The board's Maths Standard marking scheme for 2026-27 gives 1 mark for writing this AP. It gives half a mark for the equation 20 + (n - 1) × 20 = 380, and half a mark for n = 19. The last mark goes on the sum of the terms. So finding n is worth a mark before any adding starts. That is step marking at work.
Sources
Facts last checked against these sources on 30 September 2026.
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