If (14, 14-d, 14-2d, 14-3d) is an arithmetic progression, what is the common difference?
Answer and explanation
Correct answer: \(-d\)
The common difference of an arithmetic progression is obtained by subtracting a term from the next term. Here, \((14-d)-14=-d\). Also, \((14-2d)-(14-d)=-d\), so the common difference is \(-d\). Although the terms decrease by \(d\), the difference must carry a negative sign. Exam tip: always calculate common difference as next term minus previous term.
Frequently asked questions
What is the correct answer to this question?
\(-d\)
Why is this the correct answer?
The common difference of an arithmetic progression is obtained by subtracting a term from the next term. Here, \((14-d)-14=-d\). Also, \((14-2d)-(14-d)=-d\), so the common difference is \(-d\). Although the terms decrease by \(d\), the difference must carry a negative sign. Exam tip: always calculate common difference as next term minus previous term.
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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