On a stage, the rth row has 4r lamps. How many lamps will there be in 35 rows?
Answer and explanation
Correct answer: 2520
The governing concept is the sum of the first n natural numbers. Since row r contains 4r lamps, the numbers of lamps in rows 1 through 35 are 4, 8, 12, and so on, up to 4×35. Factor out 4 from the total: total lamps = 4(1+2+3+…+35). Using the formula S_n = n(n+1)/2, we get S_35 = 35×36/2 = 630. Therefore, the total number of lamps is 4×630 = 2520. Hence option D is correct. The other choices do not result from applying the natural-number sum formula and multiplying by the four lamps-per-row factor.
Frequently asked questions
What is the correct answer to this question?
2520
Why is this the correct answer?
The governing concept is the sum of the first n natural numbers. Since row r contains 4r lamps, the numbers of lamps in rows 1 through 35 are 4, 8, 12, and so on, up to 4×35. Factor out 4 from the total: total lamps = 4(1+2+3+…+35). Using the formula S_n = n(n+1)/2, we get S_35 = 35×36/2 = 630. Therefore, the total number of lamps is 4×630 = 2520. Hence option D is correct. The other choices do not result from applying the natural-number sum formula and multiplying by the four lamps-per-row factor.
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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