If each term of 13, 10, 7, 4, … is multiplied by −2, what will be the common difference of the new sequence?
Answer and explanation
Correct answer: 6
The original sequence is an AP with common difference d = 10 − 13 = −3; the next differences confirm this value. Multiplying every term by a constant multiplies the common difference by the same constant. Hence the new difference is d′ = (−2)(−3) = 6. For example, the transformed terms begin −26, −20, −14, −8, and each successive difference is 6. The negative multiplier reverses the order direction and changes the sign of the original difference, so the result is positive. Therefore option B is correct. Option C is the unchanged original difference, while the other options use an incorrect sign or magnitude.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The original sequence is an AP with common difference d = 10 − 13 = −3; the next differences confirm this value. Multiplying every term by a constant multiplies the common difference by the same constant. Hence the new difference is d′ = (−2)(−3) = 6. For example, the transformed terms begin −26, −20, −14, −8, and each successive difference is 6. The negative multiplier reverses the order direction and changes the sign of the original difference, so the result is positive. Therefore option B is correct. Option C is the unchanged original difference, while the other options use an incorrect sign or magnitude.
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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