What is the value of S₇₀ − 2S₃₅?
Answer and explanation
Correct answer: 1225
Use Sₙ = n(n + 1)/2. First, S₇₀ = 70 × 71/2 = 35 × 71 = 2485. Next, S₃₅ = 35 × 36/2 = 35 × 18 = 630, so 2S₃₅ = 2 × 630 = 1260. Therefore S₇₀ − 2S₃₅ = 2485 − 1260 = 1225, making option B correct. The coefficient 2 must be applied to the complete value of S₃₅ before subtraction. Option A or C can result from a multiplication or subtraction slip, while option D may come from mishandling the coefficient or using a wrong partial sum. Keeping the order and brackets clear prevents these errors.
Frequently asked questions
What is the correct answer to this question?
1225
Why is this the correct answer?
Use Sₙ = n(n + 1)/2. First, S₇₀ = 70 × 71/2 = 35 × 71 = 2485. Next, S₃₅ = 35 × 36/2 = 35 × 18 = 630, so 2S₃₅ = 2 × 630 = 1260. Therefore S₇₀ − 2S₃₅ = 2485 − 1260 = 1225, making option B correct. The coefficient 2 must be applied to the complete value of S₃₅ before subtraction. Option A or C can result from a multiplication or subtraction slip, while option D may come from mishandling the coefficient or using a wrong partial sum. Keeping the order and brackets clear prevents these errors.
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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