In an AP, (a_{15}=a_5+50) and (a_5=24). What is (a_{31})?
Answer and explanation
Correct answer: 154
In an AP, \(a_{15}-a_5=(15-5)d=10d\). Since \(a_{15}=a_5+50\), we get \(10d=50\), so \(d=5\). Now, \(a_{31}=a_5+(31-5)d=24+26\times5=154\). Hence, 154 is correct. Although 158 is close, it does not follow from the given common difference \(d=5\). Exam tip: When comparing two terms, use the difference between their term numbers.
Frequently asked questions
What is the correct answer to this question?
154
Why is this the correct answer?
In an AP, \(a_{15}-a_5=(15-5)d=10d\). Since \(a_{15}=a_5+50\), we get \(10d=50\), so \(d=5\). Now, \(a_{31}=a_5+(31-5)d=24+26\times5=154\). Hence, 154 is correct. Although 158 is close, it does not follow from the given common difference \(d=5\). Exam tip: When comparing two terms, use the difference between their term numbers.
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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