In an AP, (a_{20}=0) and (a_{50}=-270). What is (a_1)?
Answer and explanation
Correct answer: 171
For an AP, \(a_n=a_1+(n-1)d\). Subtracting the given terms gives \(a_{50}-a_{20}=30d=-270\), so \(d=-9\). Now \(a_{20}=a_1+19d=0\), hence \(a_1=-19(-9)=171\). If 180 were chosen, the 20th term would be 9, not 0. Exam tip: subtract two given terms first to eliminate \(a_1\) and find \(d\) quickly.
Frequently asked questions
What is the correct answer to this question?
171
Why is this the correct answer?
For an AP, \(a_n=a_1+(n-1)d\). Subtracting the given terms gives \(a_{50}-a_{20}=30d=-270\), so \(d=-9\). Now \(a_{20}=a_1+19d=0\), hence \(a_1=-19(-9)=171\). If 180 were chosen, the 20th term would be 9, not 0. Exam tip: subtract two given terms first to eliminate \(a_1\) and find \(d\) quickly.
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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