Sum of First n Terms of an AP
The sum of the first n terms of an arithmetic progression is the total obtained by adding its first n terms.
Practice This ConceptMain explanation
Teacher explanation
Instead of adding many terms one by one, we use a formula. If the first term is a and common difference is d, then Sn = n/2 × (2a + (n - 1)d). If the first and last terms are known, use Sn = n/2 × (a + l).
Example
For 2, 5, 8, 11, the sum of first 4 terms is 2 + 5 + 8 + 11 = 26.
Simple analogy
AP sum pairs the beginning and ending terms.
Common confusion
Students sometimes use the last visible term as l even when the question asks for more terms than shown.
Exam tip
Choose Sn = n/2 × (a + l) only when the last required term l is known or can be found correctly.
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