A student solves 5 questions on the first day and 2 more questions each next day. How many questions will he solve on the 12th day?
Answer and explanation
Correct answer: 27
The daily numbers form an AP: the first day's value is a = 5 and the fixed daily increase is the common difference d = 2. The day number is the term number, so for the 12th day use aₙ = a + (n − 1)d. Thus a₁₂ = 5 + (12 − 1)×2 = 5 + 11×2 = 5 + 22 = 27. Hence option C is correct. Eleven increases are needed after the first day to reach day twelve. Option A is too small, option B adds one extra increase, and option D does not follow the fixed increment of two. Listing the values as 5, 7, 9, ... also leads to 27 on day twelve.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
The daily numbers form an AP: the first day's value is a = 5 and the fixed daily increase is the common difference d = 2. The day number is the term number, so for the 12th day use aₙ = a + (n − 1)d. Thus a₁₂ = 5 + (12 − 1)×2 = 5 + 11×2 = 5 + 22 = 27. Hence option C is correct. Eleven increases are needed after the first day to reach day twelve. Option A is too small, option B adds one extra increase, and option D does not follow the fixed increment of two. Listing the values as 5, 7, 9, ... also leads to 27 on day twelve.
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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