If an arithmetic progression has (a_5=30) and (a_{12}=72), what is (d)?
Answer and explanation
Correct answer: 6
In an AP, the difference between two terms equals the difference in their positions multiplied by the common difference: \(a_{12}-a_5=(12-5)d\). Thus, \(72-30=7d\), so \(42=7d\) and \(d=6\). Choosing 7 would confuse the difference in term positions with the common difference. Exam tip: when using \(a_n=a+(n-1)d\), track the term numbers carefully.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
In an AP, the difference between two terms equals the difference in their positions multiplied by the common difference: \(a_{12}-a_5=(12-5)d\). Thus, \(72-30=7d\), so \(42=7d\) and \(d=6\). Choosing 7 would confuse the difference in term positions with the common difference. Exam tip: when using \(a_n=a+(n-1)d\), track the term numbers carefully.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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