In a saving plan, 1 rupee is saved in the 1st week and 49 rupees in the 49th week. If the amount increases by 1 rupee each week, what is the total saving?
Answer and explanation
Correct answer: 1225
The weekly amounts are 1, 2, 3, …, 49 because the saving starts at 1 rupee and increases by exactly 1 rupee each week. Thus the total is the sum of the first 49 natural numbers. Using Sₙ = n(n + 1)/2, we get S₄₉ = 49 × 50/2 = 49 × 25 = 1225 rupees. Therefore option B is correct. The arithmetic-progression form gives the same result: there are 49 terms, the first is 1 and the last is 49, so total = 49(1 + 49)/2 = 1225. Options A, C, and D result from miscounting weeks or applying the wrong average.
Frequently asked questions
What is the correct answer to this question?
1225
Why is this the correct answer?
The weekly amounts are 1, 2, 3, …, 49 because the saving starts at 1 rupee and increases by exactly 1 rupee each week. Thus the total is the sum of the first 49 natural numbers. Using Sₙ = n(n + 1)/2, we get S₄₉ = 49 × 50/2 = 49 × 25 = 1225 rupees. Therefore option B is correct. The arithmetic-progression form gives the same result: there are 49 terms, the first is 1 and the last is 49, so total = 49(1 + 49)/2 = 1225. Options A, C, and D result from miscounting weeks or applying the wrong average.
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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