In an AP, (a_7+a_{21}=224) and (a_{13}+a_{27}=368). What is (a_{41})?
Answer and explanation
Correct answer: 436
For an AP, \(a_n=a+(n-1)d\). Thus, \(a_7+a_{21}=2a+26d=224\) and \(a_{13}+a_{27}=2a+38d=368\). Subtracting the equations gives \(12d=144\), so \(d=12\). Then \(2a+26(12)=224\) gives \(a=-44\). Hence, \(a_{41}=a+40d=-44+40(12)=436\). Option 560 results from not accounting for the first term \(a\). Exam tip: in AP questions involving two sums of terms, subtract the equations first to find \(d\) quickly.
Frequently asked questions
What is the correct answer to this question?
436
Why is this the correct answer?
For an AP, \(a_n=a+(n-1)d\). Thus, \(a_7+a_{21}=2a+26d=224\) and \(a_{13}+a_{27}=2a+38d=368\). Subtracting the equations gives \(12d=144\), so \(d=12\). Then \(2a+26(12)=224\) gives \(a=-44\). Hence, \(a_{41}=a+40d=-44+40(12)=436\). Option 560 results from not accounting for the first term \(a\). Exam tip: in AP questions involving two sums of terms, subtract the equations 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.
