A student practises for 36 minutes on the first day and 7 more minutes each day. On which day will the practice time be 218 minutes?
Answer and explanation
Correct answer: 27वाँ दिन
The daily practice times form an arithmetic progression with first term a₁ = 36 and common difference d = 7. The nth-term formula is aₙ = a₁ + (n − 1)d. Since the question asks for the practice time on one day, we set the term, not the sum of all practice times, equal to 218: 218 = 36 + 7(n − 1). Thus 182 = 7(n − 1), so n − 1 = 26 and n = 27. Therefore the practice time reaches 218 minutes on the 27th day, making option C correct. The nearby choices arise from treating the first day as zero or making a one-day indexing error.
Frequently asked questions
What is the correct answer to this question?
27वाँ दिन
Why is this the correct answer?
The daily practice times form an arithmetic progression with first term a₁ = 36 and common difference d = 7. The nth-term formula is aₙ = a₁ + (n − 1)d. Since the question asks for the practice time on one day, we set the term, not the sum of all practice times, equal to 218: 218 = 36 + 7(n − 1). Thus 182 = 7(n − 1), so n − 1 = 26 and n = 27. Therefore the practice time reaches 218 minutes on the 27th day, making option C correct. The nearby choices arise from treating the first day as zero or making a one-day indexing error.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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