If (3z, z+10, 22-z) are in an arithmetic progression, what is the first term?
Answer and explanation
Correct answer: No such value of z
For three consecutive terms of an AP, twice the middle term equals the sum of the first and third terms. Thus, \(2(z+10)=3z+(22-z)\). On simplifying, the left side is \(2z+20\) and the right side is \(2z+22\), which gives \(20=22\), an impossibility. Hence, no value of \(z\) satisfies the condition, so the first term cannot be determined. Exam tip: For three AP terms, always check \(2b=a+c\).
Frequently asked questions
What is the correct answer to this question?
No such value of z
Why is this the correct answer?
For three consecutive terms of an AP, twice the middle term equals the sum of the first and third terms. Thus, \(2(z+10)=3z+(22-z)\). On simplifying, the left side is \(2z+20\) and the right side is \(2z+22\), which gives \(20=22\), an impossibility. Hence, no value of \(z\) satisfies the condition, so the first term cannot be determined. Exam tip: For three AP terms, always check \(2b=a+c\).
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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