In an AP, (a_{10}=0) and (a_{21}=-55). What is (a_1)?
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Answer and explanation
Correct answer: 45
For an AP, \(a_n=a_1+(n-1)d\). Thus, \(a_{21}-a_{10}=11d=-55\), so \(d=-5\). Now, using \(a_{10}=a_1+9d\), we get \(0=a_1+9(-5)\), hence \(a_1=45\). If 40 were chosen, the tenth term would be \(-5\), not the given value 0. Exam tip: When two terms are given, subtract them first to find \(d\) quickly.
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
For an AP, \(a_n=a_1+(n-1)d\). Thus, \(a_{21}-a_{10}=11d=-55\), so \(d=-5\). Now, using \(a_{10}=a_1+9d\), we get \(0=a_1+9(-5)\), hence \(a_1=45\). If 40 were chosen, the tenth term would be \(-5\), not the given value 0. Exam tip: When two terms are given, subtract them first to 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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