If (6,10,n,18) are consecutive terms of an arithmetic progression, what is (n)?
Answer and explanation
Correct answer: (14)
In an arithmetic progression, the common difference is the same between every pair of consecutive terms. The first two terms here are 6 and 10, so \(d=10-6=4\). The third term is obtained by adding this difference to the second term: \(n=10+4=14\). The fourth term then becomes \(14+4=18\), which confirms that the sequence is consistent.
Therefore \(n=14\), so option D is correct. Another way to see this is that the middle term of four consecutive terms is equally spaced: the terms move from 6 to 10, then to 14, and then to 18. The values 12, 13, and 15 do not preserve the same difference throughout the progression.
Frequently asked questions
What is the correct answer to this question?
(14)
Why is this the correct answer?
In an arithmetic progression, the common difference is the same between every pair of consecutive terms. The first two terms here are 6 and 10, so \(d=10-6=4\). The third term is obtained by adding this difference to the second term: \(n=10+4=14\). The fourth term then becomes \(14+4=18\), which confirms that the sequence is consistent.
Therefore \(n=14\), so option D is correct. Another way to see this is that the middle term of four consecutive terms is equally spaced: the terms move from 6 to 10, then to 14, and then to 18. The values 12, 13, and 15 do not preserve the same difference throughout the progression.
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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