If (5-2t, 7-t, 12+t) are in an arithmetic progression, what is the value of (t)?
Answer and explanation
Correct answer: -3
In an arithmetic progression, the differences between consecutive terms are equal. The first difference is \((7-t)-(5-2t)=t+2\), and the second difference is \((12+t)-(7-t)=5+2t\). Thus, \(t+2=5+2t\), which gives \(t=-3\). Substituting \(-2\) does not make the two differences equal. Exam tip: for three AP terms, you can also check whether twice the middle term equals the sum of the first and third terms.
Frequently asked questions
What is the correct answer to this question?
-3
Why is this the correct answer?
In an arithmetic progression, the differences between consecutive terms are equal. The first difference is \((7-t)-(5-2t)=t+2\), and the second difference is \((12+t)-(7-t)=5+2t\). Thus, \(t+2=5+2t\), which gives \(t=-3\). Substituting \(-2\) does not make the two differences equal. Exam tip: for three AP terms, you can also check whether twice the middle term equals the sum of the first and third terms.
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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