In an AP (a_{10}=58) and (a_{22}=130). What is the first term?
Answer and explanation
Correct answer: 4
For an AP, \(a_n=a+(n-1)d\). Thus, \(a_{22}-a_{10}=12d=130-58=72\), so \(d=6\). Now \(a_{10}=a+9d\) gives \(58=a+9\times6\), hence \(a=4\). Option 6 is the common difference, not the first term. Exam tip: When two terms are given, first use the difference in their term numbers to find \(d\).
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For an AP, \(a_n=a+(n-1)d\). Thus, \(a_{22}-a_{10}=12d=130-58=72\), so \(d=6\). Now \(a_{10}=a+9d\) gives \(58=a+9\times6\), hence \(a=4\). Option 6 is the common difference, not the first term. Exam tip: When two terms are given, first use the difference in their term numbers 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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