What is the first term greater than 850 in the AP 27, 40, 53, ...?
Answer and explanation
Correct answer: 859
The first term is a₁ = 27 and the common difference is d = 40 − 27 = 13. Thus the nth term is aₙ = 27 + (n − 1)13. To locate the point around 850, solve 27 + 13(n − 1) > 850, giving 13(n − 1) > 823 and n − 1 > 63.307..., so the least integer n is 65. The corresponding term is a₆₅ = 27 + 64 × 13 = 27 + 832 = 859. The preceding term is a₆₄ = 846, which is not greater than 850. Therefore option B is the first valid term; later options are also greater but are not the first one.
Frequently asked questions
What is the correct answer to this question?
859
Why is this the correct answer?
The first term is a₁ = 27 and the common difference is d = 40 − 27 = 13. Thus the nth term is aₙ = 27 + (n − 1)13. To locate the point around 850, solve 27 + 13(n − 1) > 850, giving 13(n − 1) > 823 and n − 1 > 63.307..., so the least integer n is 65. The corresponding term is a₆₅ = 27 + 64 × 13 = 27 + 832 = 859. The preceding term is a₆₄ = 846, which is not greater than 850. Therefore option B is the first valid term; later options are also greater but are not the first one.
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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