If (4, r, s, 31) are in an arithmetic progression, what is the value of s−r?
Answer and explanation
Correct answer: 9
In a four-term arithmetic progression, the change from the first term to the fourth term contains three equal common differences. Let the common difference be d. Then 4+3d=31, so 3d=27 and d=9. Since r is the second term and s is the third term, their difference is s−r=d=9. Equivalently, the terms are 4, 13, 22, and 31, which confirms the result directly. Therefore option C is correct. The number 27 is the total change from the first to fourth term, not the difference between adjacent terms, so it is not an answer choice.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
In a four-term arithmetic progression, the change from the first term to the fourth term contains three equal common differences. Let the common difference be d. Then 4+3d=31, so 3d=27 and d=9. Since r is the second term and s is the third term, their difference is s−r=d=9. Equivalently, the terms are 4, 13, 22, and 31, which confirms the result directly. Therefore option C is correct. The number 27 is the total change from the first to fourth term, not the difference between adjacent terms, so it is not an answer choice.
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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