Nth term of an AP
The nth term of an AP is the formula used to find any term directly without writing all the earlier terms.
Practice This ConceptMain explanation
Teacher explanation
The nth term formula saves time in exams because it gives the required term in one step. For an AP with first term a and common difference d, the nth term is found by starting from the first term and adding the common difference one less time than the term number.
Example
For 5, 9, 13, 17, ... the 4th term is 5 + 3(4 - 1) = 14.
Simple analogy
First term plus one less set of jumps than the term number.
Common confusion
Students often use n instead of n - 1, which gives one extra common difference.
Exam tip
Write the formula first, then substitute a, d, and n carefully before simplifying.
Answer writing and exam use
1-mark use
Write the exact meaning of nth term of an ap in one clean line.
2-mark use
Define nth term of an ap and add one example or condition.
3-mark use
Explain nth term of an ap, show the method or example, and mention the common mistake.
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