If Sₙ = 1225, what is the value of n?
Answer and explanation
Correct answer: 49
Direct answer: n = 49, so option C is correct. Here Sₙ means the sum 1 + 2 + 3 + ... + n. The formula is Sₙ = n(n + 1)/2. Substitute the given sum: n(n + 1)/2 = 1225, so n(n + 1) = 2450. Now test the natural neighboring value 49: 49 × 50 = 2450. Hence S₄₉ = 49 × 50/2 = 49 × 25 = 1225. Therefore option C is correct. To reject the other choices, calculate their sums: S₄₇ = 47 × 48/2 = 1128, S₄₈ = 48 × 49/2 = 1176, and S₅₀ = 50 × 51/2 = 1275. None equals 1225. The sum increases whenever n increases because a new positive natural number is added, so there cannot be another listed value with the same sum. Common warning: do not solve n(n + 1) = 1225; the factor 2 must be handled first.
Frequently asked questions
What is the correct answer to this question?
49
Why is this the correct answer?
Direct answer: n = 49, so option C is correct. Here Sₙ means the sum 1 + 2 + 3 + ... + n. The formula is Sₙ = n(n + 1)/2. Substitute the given sum: n(n + 1)/2 = 1225, so n(n + 1) = 2450. Now test the natural neighboring value 49: 49 × 50 = 2450. Hence S₄₉ = 49 × 50/2 = 49 × 25 = 1225. Therefore option C is correct. To reject the other choices, calculate their sums: S₄₇ = 47 × 48/2 = 1128, S₄₈ = 48 × 49/2 = 1176, and S₅₀ = 50 × 51/2 = 1275. None equals 1225. The sum increases whenever n increases because a new positive natural number is added, so there cannot be another listed value with the same sum. Common warning: do not solve n(n + 1) = 1225; the factor 2 must be handled first.
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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