Finding n when sum is known
Finding n when sum is known means using the sum formula to determine how many terms of an AP add up to a given total.
Practice This ConceptMain explanation
Teacher explanation
Sometimes the exam gives the total sum and asks for the number of terms. In such questions, students must set up the sum formula, substitute the known values, and solve the resulting equation for n. This often creates a quadratic equation, so neat algebra is important.
Example
If the sum of an AP is 30 and the terms are 2, 4, 6, 8, ..., then n = 5 because 2 + 4 + 6 + 8 + 10 = 30.
Simple analogy
When the total is known, n is the hidden count you must uncover.
Common confusion
Students may use the nth-term formula instead of the sum formula when the question is about total sum.
Exam tip
If the phrase says sum, total, or altogether, start with the sum formula.
Answer writing and exam use
1-mark use
Write the exact meaning of finding n when sum is known in one clean line.
2-mark use
Define finding n when sum is known and add one example or condition.
3-mark use
Explain finding n when sum is known, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
Help improve this page
Found something confusing, incorrect, or missing?