If (10, 10+d, 10+2d, 10+4d) is an arithmetic progression, which conclusion is correct?
Answer and explanation
Correct answer: \(d=0\)
The consecutive differences are \((10+d)-10=d\), \((10+2d)-(10+d)=d\), and \((10+4d)-(10+2d)=2d\). In an arithmetic progression, all consecutive differences must be equal. Thus, \(d=2d\), which gives \(d=0\). If \(d=2\) or \(d=4\), the last difference becomes 4 or 8 respectively, so it is not equal to the earlier difference. Exam tip: To test an AP, compare the differences between consecutive terms.
Frequently asked questions
What is the correct answer to this question?
\(d=0\)
Why is this the correct answer?
The consecutive differences are \((10+d)-10=d\), \((10+2d)-(10+d)=d\), and \((10+4d)-(10+2d)=2d\). In an arithmetic progression, all consecutive differences must be equal. Thus, \(d=2d\), which gives \(d=0\). If \(d=2\) or \(d=4\), the last difference becomes 4 or 8 respectively, so it is not equal to the earlier difference. Exam tip: To test an AP, compare the differences between consecutive terms.
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..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
