Q1
The nth term formula for an AP is:
Aa+(n-1)d
Ba x n x d
Ca+n+d
Da/(n-1)
CBSEClass 10 (CBSE)MathematicsCh 5 · Topic 1
nth Term of an AP
Learning to find any term of an arithmetic progression using a formula.
Core concept
For example, in the AP 2, 5, 8, 11... (first term a=2, common difference d=3), the 10th term is calculated as a₁₀ = 2 + (10-1)×3 = 2+27 = 29. This formula allows finding any term in a sequence directly, without needing to list out and add up all the preceding terms one by one, making it especially useful for finding terms far into a long sequence, or for solving real-world problems involving regular patterns, like monthly savings that increase by a fixed amount each month.
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• The nth term formula for an AP is: aₙ = a + (n-1)d.
• 'a' is the first term, 'd' is the common difference, 'n' is the term's position.
• Example: for AP 2,5,8,11..., the 10th term is 2+(10-1)x3 = 29.
• This formula avoids the need to list all preceding terms to find a distant term.