If (5,11,n,23) are consecutive terms of an arithmetic progression, what is (n)?
Answer and explanation
Correct answer: (17)
For consecutive terms of an arithmetic progression, the difference between adjacent terms is constant. From the first two terms, the common difference is \(d=11-5=6\). Add this difference to the second term to obtain the third term: \(n=11+6=17\). Adding 6 once more gives \(17+6=23\), matching the fourth term and confirming the calculation.
Therefore \(n=17\), so option C is correct. The sequence is \(5,11,17,23\), and each term increases by 6. Values such as 15 or 16 would make the differences unequal, while 18 would produce a third-to-fourth difference of only 5. Hence only 17 satisfies the arithmetic-progression condition.
Frequently asked questions
What is the correct answer to this question?
(17)
Why is this the correct answer?
For consecutive terms of an arithmetic progression, the difference between adjacent terms is constant. From the first two terms, the common difference is \(d=11-5=6\). Add this difference to the second term to obtain the third term: \(n=11+6=17\). Adding 6 once more gives \(17+6=23\), matching the fourth term and confirming the calculation.
Therefore \(n=17\), so option C is correct. The sequence is \(5,11,17,23\), and each term increases by 6. Values such as 15 or 16 would make the differences unequal, while 18 would produce a third-to-fourth difference of only 5. Hence only 17 satisfies the arithmetic-progression condition.
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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