In a triangular decoration, flowers are arranged in rows from 1 to 28. How many flowers are there in total?
Answer and explanation
Correct answer: 406
A triangular arrangement with rows containing 1, 2, 3, …, 28 flowers has a total equal to the 28th triangular number. The governing formula is Sₙ = n(n + 1)/2, so S₂₈ = 28 × 29/2 = 14 × 29 = 406. Therefore option B is correct. The word triangular indicates that each new row contributes the next natural number, not that the area of a geometric triangle must be calculated. Option A is smaller than the correct total, while options C and D arise from adding an extra amount or using an incorrect endpoint. Counting the 28 rows and applying the triangular-number formula gives the total directly.
Frequently asked questions
What is the correct answer to this question?
406
Why is this the correct answer?
A triangular arrangement with rows containing 1, 2, 3, …, 28 flowers has a total equal to the 28th triangular number. The governing formula is Sₙ = n(n + 1)/2, so S₂₈ = 28 × 29/2 = 14 × 29 = 406. Therefore option B is correct. The word triangular indicates that each new row contributes the next natural number, not that the area of a geometric triangle must be calculated. Option A is smaller than the correct total, while options C and D arise from adding an extra amount or using an incorrect endpoint. Counting the 28 rows and applying the triangular-number formula gives the total directly.
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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