Which term of the AP (21, 29, 37, ...) is 149?
Answer and explanation
Correct answer: 17th
The nth-term rule for an arithmetic progression is a_n = a + (n − 1)d. Here a = 21 and d = 29 − 21 = 8. Set the nth term equal to the given value 149: 149 = 21 + (n − 1)8. Subtracting 21 gives 128 = 8(n − 1), so n − 1 = 16 and n = 17. Therefore 149 is the 17th term, making option C correct. The result is easily verified: the 17th term is 21 + 16 × 8 = 21 + 128 = 149. The 16th term is 141 and the 18th term is 157, so the adjacent choices cannot be correct. The factor n − 1 is necessary because the first term already corresponds to n = 1.
Frequently asked questions
What is the correct answer to this question?
17th
Why is this the correct answer?
The nth-term rule for an arithmetic progression is a_n = a + (n − 1)d. Here a = 21 and d = 29 − 21 = 8. Set the nth term equal to the given value 149: 149 = 21 + (n − 1)8. Subtracting 21 gives 128 = 8(n − 1), so n − 1 = 16 and n = 17. Therefore 149 is the 17th term, making option C correct. The result is easily verified: the 17th term is 21 + 16 × 8 = 21 + 128 = 149. The 16th term is 141 and the 18th term is 157, so the adjacent choices cannot be correct. The factor n − 1 is necessary because the first term already corresponds to n = 1.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
