Which sum is formed when 38 and 39 are added to 1 + 2 + 3 + ⋯ + 37?
Answer and explanation
Correct answer: S₃₉
The governing idea is the definition of a partial sum: Sₘ = 1 + 2 + 3 + ⋯ + m. The expression already contains every natural number from 1 through 37. Adding the next consecutive terms, 38 and 39, produces 1 + 2 + ⋯ + 37 + 38 + 39, which is exactly the sum of the first 39 natural numbers, S₃₉. Thus option C is correct. It is not S₃₈ because that would stop after adding 38, and it is not S₄₀ because the term 40 has not been included. Option A ignores both added terms. The important step is to track the largest included natural number, not to add the numerical values 38 and 39 to the subscript.
Frequently asked questions
What is the correct answer to this question?
S₃₉
Why is this the correct answer?
The governing idea is the definition of a partial sum: Sₘ = 1 + 2 + 3 + ⋯ + m. The expression already contains every natural number from 1 through 37. Adding the next consecutive terms, 38 and 39, produces 1 + 2 + ⋯ + 37 + 38 + 39, which is exactly the sum of the first 39 natural numbers, S₃₉. Thus option C is correct. It is not S₃₈ because that would stop after adding 38, and it is not S₄₀ because the term 40 has not been included. Option A ignores both added terms. The important step is to track the largest included natural number, not to add the numerical values 38 and 39 to the subscript.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
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