In an AP, (a_{12}=0) and (a_{28}=-96). What is (a_1)?
Answer and explanation
Correct answer: 66
For an AP, \(a_n=a_1+(n-1)d\). Thus, \(a_{28}-a_{12}=16d=-96\), so \(d=-6\). Now \(a_{12}=a_1+11d=0\) gives \(a_1=-11(-6)=66\). Therefore, 66 is the correct option. If 60 were chosen, \(a_{12}\) would be \(-6\), not the given value. Exam tip: when two terms are given, first find \(d\) by subtracting the terms.
Frequently asked questions
What is the correct answer to this question?
66
Why is this the correct answer?
For an AP, \(a_n=a_1+(n-1)d\). Thus, \(a_{28}-a_{12}=16d=-96\), so \(d=-6\). Now \(a_{12}=a_1+11d=0\) gives \(a_1=-11(-6)=66\). Therefore, 66 is the correct option. If 60 were chosen, \(a_{12}\) would be \(-6\), not the given value. Exam tip: when two terms are given, first find \(d\) by subtracting the terms.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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