If (-4, s, 8, 14) are consecutive terms of an arithmetic progression, what will (s) be?
Answer and explanation
Correct answer: (2)
In an arithmetic progression, every consecutive pair has the same common difference. The given consecutive terms are \(-4,s,8,14\). From 8 to 14, the difference is \(14-8=6\), so the common difference must be 6 throughout the progression. Moving one step backward from 8 means subtracting 6, giving \(s=8-6=2\). Therefore, option B is correct.
This can also be checked from the first terms: \(s-(-4)=s+4\) must equal 6, so \(s=2\). Then the sequence becomes \(-4,2,8,14\), whose consecutive differences are all 6. The value 0 would make the first difference 4, and 4 would make it 8; neither agrees with the difference between 8 and 14. Thus 2 is the only suitable value.
Frequently asked questions
What is the correct answer to this question?
(2)
Why is this the correct answer?
In an arithmetic progression, every consecutive pair has the same common difference. The given consecutive terms are \(-4,s,8,14\). From 8 to 14, the difference is \(14-8=6\), so the common difference must be 6 throughout the progression. Moving one step backward from 8 means subtracting 6, giving \(s=8-6=2\). Therefore, option B is correct.
This can also be checked from the first terms: \(s-(-4)=s+4\) must equal 6, so \(s=2\). Then the sequence becomes \(-4,2,8,14\), whose consecutive differences are all 6. The value 0 would make the first difference 4, and 4 would make it 8; neither agrees with the difference between 8 and 14. Thus 2 is the only suitable value.
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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