The sequence (7, x, 23, y, 39) is an arithmetic progression. What is the value of (x+y)?
Answer and explanation
Correct answer: 46
In an arithmetic progression, consecutive terms have the same difference. There are 4 gaps between the first and fifth terms, so the common difference is \(d=\frac{39-7}{4}=8\). Thus, \(x=7+8=15\) and \(y=23+8=31\). Therefore, \(x+y=15+31=46\). Option 42 can result from counting the gaps incorrectly. Exam tip: between \(n\) terms, there are always \(n-1\) gaps.
Frequently asked questions
What is the correct answer to this question?
46
Why is this the correct answer?
In an arithmetic progression, consecutive terms have the same difference. There are 4 gaps between the first and fifth terms, so the common difference is \(d=\frac{39-7}{4}=8\). Thus, \(x=7+8=15\) and \(y=23+8=31\). Therefore, \(x+y=15+31=46\). Option 42 can result from counting the gaps incorrectly. Exam tip: between \(n\) terms, there are always \(n-1\) gaps.
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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