What will be the 24th term of the AP (−15, −9, −3, ...)?
Answer and explanation
Correct answer: 123
For an arithmetic progression, use a_n = a + (n − 1)d. The first term is a = −15, and the common difference is d = −9 − (−15) = 6. Substituting n = 24 gives a_24 = −15 + (24 − 1)6 = −15 + 23 × 6 = −15 + 138 = 123. Thus option B is correct. The negative sign belongs to the first term, while the common difference is positive because the sequence increases by 6 each time. A likely mistake is to write −15 + 24 × 6, which counts one extra gap and gives 129, or to mishandle the negative first term. Checking the sequence rule confirms that 23 jumps from the first term lead to the 24th term.
Frequently asked questions
What is the correct answer to this question?
123
Why is this the correct answer?
For an arithmetic progression, use a_n = a + (n − 1)d. The first term is a = −15, and the common difference is d = −9 − (−15) = 6. Substituting n = 24 gives a_24 = −15 + (24 − 1)6 = −15 + 23 × 6 = −15 + 138 = 123. Thus option B is correct. The negative sign belongs to the first term, while the common difference is positive because the sequence increases by 6 each time. A likely mistake is to write −15 + 24 × 6, which counts one extra gap and gives 129, or to mishandle the negative first term. Checking the sequence rule confirms that 23 jumps from the first term lead to the 24th term.
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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