If the opposite of each term of (9,5,1,-3,\ldots) is taken, what will be (d) of the new sequence?
Answer and explanation
Correct answer: \(4\)
The common difference of the original sequence is \(5-9=-4\). Taking the opposite of every term gives \((-9,-5,-1,3,\ldots)\). The difference between consecutive terms is \(-5-(-9)=4\), so the new common difference is \(4\). The value \(-4\) is the common difference of the original sequence, not the new one. Exam tip: when every term is multiplied by \(-1\), the sign of the common difference also changes.
Frequently asked questions
What is the correct answer to this question?
\(4\)
Why is this the correct answer?
The common difference of the original sequence is \(5-9=-4\). Taking the opposite of every term gives \((-9,-5,-1,3,\ldots)\). The difference between consecutive terms is \(-5-(-9)=4\), so the new common difference is \(4\). The value \(-4\) is the common difference of the original sequence, not the new one. Exam tip: when every term is multiplied by \(-1\), the sign of the common difference also changes.
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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