Common difference
- CBSE · NCERT Class 10, Ch 5 Arithmetic Progressions
The common difference of an arithmetic progression is the fixed amount added to each term to get the next one.
It is written d. You find it as d = a₂ - a₁, the second term minus the first. Any term minus the one before it gives the same d. The order matters: subtracting the other way round flips the sign.
The sign of d tells you the direction of an arithmetic progression. If d is positive, the terms grow. If it is negative, they shrink. If d = 0, every term is the same.
A small example
- For 10, 7, 4, 1, ...: d = 7 - 10 = -3. The terms fall by 3 each time.
- For -5, -1, 3, 7, ...: d = -1 - (-5) = -1 + 5 = 4.
- For 1/2, 1, 3/2, 2, ...: d = 1/2.
Where marks go
Question 5 of CBSE's 2026-27 Maths Standard sample paper asks for the middle term of 10, 7, 4, ..., -62. The board's Maths Standard marking scheme for 2026-27 first uses d = -3 to find that the AP has 25 terms. The middle one is then the 13th term, which is -26. With d taken as +3, every later step gives a different answer.
That question is a 1-mark multiple-choice question with no part marks. Question 37 of the 2026-27 Maths Basic sample paper is one of its case-based questions. There the common difference is part (i) on its own, worth 1 mark.
Sources
Facts last checked against these sources on 30 September 2026.
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