In the AP (97,88,79,...), what is the first term less than (20)?
Answer and explanation
Correct answer: (16)
The sequence is an arithmetic progression because the difference between consecutive terms is constant. Here the common difference is \(d = 88 - 97 = -9\), so every next term is 9 less than the preceding term. Since the sequence decreases, we can list terms near 20 or use the nth-term formula \(a_n = 97 + (n-1)(-9)\). We need the first term that is strictly less than 20.
The terms descend as 97, 88, 79, 70, 61, 52, 43, 34, 25, 16, 7, and so on. The term 25 is still greater than 20, while the next term, 16, is less than 20. Therefore the first required term is 16, so option A is correct. The number 18 is not in this progression because its terms change by 9 each time.
Frequently asked questions
What is the correct answer to this question?
(16)
Why is this the correct answer?
The sequence is an arithmetic progression because the difference between consecutive terms is constant. Here the common difference is \(d = 88 - 97 = -9\), so every next term is 9 less than the preceding term. Since the sequence decreases, we can list terms near 20 or use the nth-term formula \(a_n = 97 + (n-1)(-9)\). We need the first term that is strictly less than 20.
The terms descend as 97, 88, 79, 70, 61, 52, 43, 34, 25, 16, 7, and so on. The term 25 is still greater than 20, while the next term, 16, is less than 20. Therefore the first required term is 16, so option A is correct. The number 18 is not in this progression because its terms change by 9 each time.
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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