Sum of first n terms
The sum of first n terms of an AP is the total obtained by adding the first n terms of the sequence.
Practice This ConceptMain explanation
Teacher explanation
This idea helps in questions where a total amount, total score, total money, or total objects is asked. The sum formula is powerful because it avoids writing all terms one by one. Students must remember that the formula uses the first term, the common difference, and the number of terms.
Example
For 1, 3, 5, 7, the sum of the first 4 terms is 16.
Simple analogy
Sum means add all the required terms, not just the last one.
Common confusion
Students often mix up the formulas for nth term and sum of n terms.
Exam tip
Before solving, ask yourself whether the question wants one term or the total of many terms.
Answer writing and exam use
1-mark use
Write the exact meaning of sum of first n terms in one clean line.
2-mark use
Define sum of first n terms and add one example or condition.
3-mark use
Explain sum of first n terms, show the method or example, and mention the common mistake.
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