If (p, 11, 15, 19, ...) is an arithmetic progression, what is the value of p?
Answer and explanation
Correct answer: 7
The governing concept is that consecutive terms of an arithmetic progression differ by a constant common difference d. From the known terms, d = 15 - 11 = 4, and this is confirmed because 19 - 15 = 4. The term before 11 must therefore be obtained by moving one step backward and subtracting the same difference: p = 11 - 4 = 7. Thus option C is correct. Option A would result from subtracting 8, option B from subtracting 6, and option D from subtracting only 2; none preserves the constant difference of 4 throughout the sequence.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The governing concept is that consecutive terms of an arithmetic progression differ by a constant common difference d. From the known terms, d = 15 - 11 = 4, and this is confirmed because 19 - 15 = 4. The term before 11 must therefore be obtained by moving one step backward and subtracting the same difference: p = 11 - 4 = 7. Thus option C is correct. Option A would result from subtracting 8, option B from subtracting 6, and option D from subtracting only 2; none preserves the constant difference of 4 throughout the sequence.
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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