If (p, 18, 25, 32, ...) is an arithmetic progression, what is the value of p?
Answer and explanation
Correct answer: 11
An arithmetic progression has the same common difference between every pair of consecutive terms. From the known part, d = 25 - 18 = 7, and 32 - 25 = 7 confirms that value. To find the term immediately before 18, move one place backward in the progression and subtract d: p = 18 - 7 = 11. Therefore option C is correct. Choosing 9 or 10 would create a difference of 9 or 8 before 18, while choosing 12 would create a difference of 6. Each of those choices would break the constant-difference rule, so they cannot be the missing first term.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
An arithmetic progression has the same common difference between every pair of consecutive terms. From the known part, d = 25 - 18 = 7, and 32 - 25 = 7 confirms that value. To find the term immediately before 18, move one place backward in the progression and subtract d: p = 18 - 7 = 11. Therefore option C is correct. Choosing 9 or 10 would create a difference of 9 or 8 before 18, while choosing 12 would create a difference of 6. Each of those choices would break the constant-difference rule, so they cannot be the missing first 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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