Find the 17th term of the AP (38, 33, 28, ...).
Answer and explanation
Correct answer: −42
Use the nth-term formula a_n = a + (n − 1)d. The first term is a = 38, and the common difference is d = 33 − 38 = −5. For n = 17, a_17 = 38 + (17 − 1)(−5) = 38 + 16(−5) = 38 − 80 = −42. Hence option A is correct. The negative difference must be retained because the AP decreases by 5 at each step. A frequent error is to use +5, which would produce a positive result, or to multiply by 17 instead of 16. Checking by counting 16 decreases from 38 gives 38 − 80 = −42. The neighboring options do not satisfy the formula for the 17th position.
Frequently asked questions
What is the correct answer to this question?
−42
Why is this the correct answer?
Use the nth-term formula a_n = a + (n − 1)d. The first term is a = 38, and the common difference is d = 33 − 38 = −5. For n = 17, a_17 = 38 + (17 − 1)(−5) = 38 + 16(−5) = 38 − 80 = −42. Hence option A is correct. The negative difference must be retained because the AP decreases by 5 at each step. A frequent error is to use +5, which would produce a positive result, or to multiply by 17 instead of 16. Checking by counting 16 decreases from 38 gives 38 − 80 = −42. The neighboring options do not satisfy the formula for the 17th position.
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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