On a stage, row 1 has 3 lamps, row 2 has 6 lamps, and row 30 has 90 lamps. If row r has 3r lamps, how many lamps are there in total?
Answer and explanation
Correct answer: 1395
The number of lamps in row r is 3r, so the total for rows 1 through 30 is 3(1 + 2 + ... + 30) = 3S₃₀. Using S₃₀ = 30 × 31/2 = 15 × 31 = 465, the total is 3 × 465 = 1395. Therefore option A is correct. This is an application of the sum of the first n natural numbers with a constant multiplier. The multiplier 3 can be factored outside the sum; it should not be added as a separate row or applied only to the final row. The other options result from arithmetic slips or from using an incorrect value for S₃₀.
Frequently asked questions
What is the correct answer to this question?
1395
Why is this the correct answer?
The number of lamps in row r is 3r, so the total for rows 1 through 30 is 3(1 + 2 + ... + 30) = 3S₃₀. Using S₃₀ = 30 × 31/2 = 15 × 31 = 465, the total is 3 × 465 = 1395. Therefore option A is correct. This is an application of the sum of the first n natural numbers with a constant multiplier. The multiplier 3 can be factored outside the sum; it should not be added as a separate row or applied only to the final row. The other options result from arithmetic slips or from using an incorrect value for S₃₀.
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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