In an AP, (a_{19}=a_8+99) and (a_8=46). What is (a_{52})?
Answer and explanation
Correct answer: 442
In an AP, \(a_{19}-a_8=(19-8)d=11d\). Since \(a_{19}=a_8+99\), we get \(11d=99\), so \(d=9\). Now, \(a_{52}=a_8+(52-8)d=46+44\times9=46+396=442\). Therefore, the correct answer is \(442\). An option such as \(436\) results from not adding the correct number of common differences. Exam tip: when two terms are given, first use the difference in their indices to find \(d\).
Frequently asked questions
What is the correct answer to this question?
442
Why is this the correct answer?
In an AP, \(a_{19}-a_8=(19-8)d=11d\). Since \(a_{19}=a_8+99\), we get \(11d=99\), so \(d=9\). Now, \(a_{52}=a_8+(52-8)d=46+44\times9=46+396=442\). Therefore, the correct answer is \(442\). An option such as \(436\) results from not adding the correct number of common differences. Exam tip: when two terms are given, first use the difference in their indices to find \(d\).
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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