Which term of the AP (3, 8, 13, ...) is 88?
Answer and explanation
Correct answer: 18th
The governing formula for the nth term of an arithmetic progression is a_n = a + (n − 1)d. Here the first term is a = 3 and the common difference is d = 8 − 3 = 5. To find the position of 88, substitute a_n = 88: 88 = 3 + (n − 1)5. Thus 85 = 5(n − 1), so n − 1 = 17 and n = 18. Hence 88 is the 18th term, making option A correct. The other options result from an off-by-one error or from treating the first term as position zero. A quick check confirms the answer: the 18th term is 3 + 17 × 5 = 88, while the 17th and 19th terms are 83 and 93 respectively.
Frequently asked questions
What is the correct answer to this question?
18th
Why is this the correct answer?
The governing formula for the nth term of an arithmetic progression is a_n = a + (n − 1)d. Here the first term is a = 3 and the common difference is d = 8 − 3 = 5. To find the position of 88, substitute a_n = 88: 88 = 3 + (n − 1)5. Thus 85 = 5(n − 1), so n − 1 = 17 and n = 18. Hence 88 is the 18th term, making option A correct. The other options result from an off-by-one error or from treating the first term as position zero. A quick check confirms the answer: the 18th term is 3 + 17 × 5 = 88, while the 17th and 19th terms are 83 and 93 respectively.
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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