If in an AP a = 17, d = 9, and aₙ = 170, what is the value of n?
Answer and explanation
Correct answer: 18
The governing formula is aₙ = a + (n − 1)d, where a is the first term and d is the common difference. Substituting the given values gives 170 = 17 + (n − 1)9. Subtracting 17 from both sides, 153 = 9(n − 1). Dividing by 9 gives n − 1 = 17, so n = 18. Therefore option C is correct. The extra 1 is important: 17 differences carry the first term to the 18th term, not the 17th term. Options A and B reflect forgetting or mishandling this index adjustment, while D adds one too many steps.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The governing formula is aₙ = a + (n − 1)d, where a is the first term and d is the common difference. Substituting the given values gives 170 = 17 + (n − 1)9. Subtracting 17 from both sides, 153 = 9(n − 1). Dividing by 9 gives n − 1 = 17, so n = 18. Therefore option C is correct. The extra 1 is important: 17 differences carry the first term to the 18th term, not the 17th term. Options A and B reflect forgetting or mishandling this index adjustment, while D adds one too many steps.
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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