What is the next term in the sequence (-10,-7,-4,-1,\ldots)?
Answer and explanation
Correct answer: 2
First identify the common difference by subtracting consecutive terms. We have −7 − (−10) = 3, −4 − (−7) = 3, and −1 − (−4) = 3. Therefore this is an arithmetic progression with d = 3. To obtain the next term, add the same difference to the last displayed term: −1 + 3 = 2. Hence option A is correct. Option B would result from adding 2 instead of the established difference; option C moves in the wrong direction and ignores that the sequence is increasing; and option D adds 4. Careful handling of the negative sign is important: subtracting a negative number is equivalent to adding its positive value.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
First identify the common difference by subtracting consecutive terms. We have −7 − (−10) = 3, −4 − (−7) = 3, and −1 − (−4) = 3. Therefore this is an arithmetic progression with d = 3. To obtain the next term, add the same difference to the last displayed term: −1 + 3 = 2. Hence option A is correct. Option B would result from adding 2 instead of the established difference; option C moves in the wrong direction and ignores that the sequence is increasing; and option D adds 4. Careful handling of the negative sign is important: subtracting a negative number is equivalent to adding its positive value.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..
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