If (x−5, x+3, x+11, x+19) is an arithmetic progression, what are the differences of the first two and last two terms?
Answer and explanation
Correct answer: 8 and 8
Subtract consecutive terms directly. The difference of the first two terms is (x+3)−(x−5)=x+3−x+5=8. The difference of the last two terms is (x+19)−(x+11)=x+19−x−11=8. The variable x cancels in both calculations, so both differences are the same constant, 8. This also confirms that the displayed sequence is an arithmetic progression with common difference 8. Therefore option A is correct. Options involving x incorrectly treat the variable part as an uncancelled contribution, while 6 and 10 do not match either subtraction.
Frequently asked questions
What is the correct answer to this question?
8 and 8
Why is this the correct answer?
Subtract consecutive terms directly. The difference of the first two terms is (x+3)−(x−5)=x+3−x+5=8. The difference of the last two terms is (x+19)−(x+11)=x+19−x−11=8. The variable x cancels in both calculations, so both differences are the same constant, 8. This also confirms that the displayed sequence is an arithmetic progression with common difference 8. Therefore option A is correct. Options involving x incorrectly treat the variable part as an uncancelled contribution, while 6 and 10 do not match either subtraction.
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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