In an AP, (a_8+a_{24}=320) and (a_{14}+a_{30}=512). What is (a_{46})?
Answer and explanation
Correct answer: 640
For an AP, \(a_n=a+(n-1)d\). Hence, \(a_8+a_{24}=2a+30d=320\) and \(a_{14}+a_{30}=2a+42d=512\). Subtracting the equations gives \(12d=192\), so \(d=16\). Then \(2a+30(16)=320\), giving \(a=-80\). Therefore, \(a_{46}=a+45d=-80+45(16)=640\). A common mistake is to use \(46d\) instead of \((46-1)d\) in the term formula. Exam tip: when sums of AP terms are given, form both linear equations and subtract them first.
Frequently asked questions
What is the correct answer to this question?
640
Why is this the correct answer?
For an AP, \(a_n=a+(n-1)d\). Hence, \(a_8+a_{24}=2a+30d=320\) and \(a_{14}+a_{30}=2a+42d=512\). Subtracting the equations gives \(12d=192\), so \(d=16\). Then \(2a+30(16)=320\), giving \(a=-80\). Therefore, \(a_{46}=a+45d=-80+45(16)=640\). A common mistake is to use \(46d\) instead of \((46-1)d\) in the term formula. Exam tip: when sums of AP terms are given, form both linear equations and subtract them first.
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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