In an AP, (a_3=4) and (a_6=25). What is the common difference?
Answer and explanation
Correct answer: 7
In an AP, the difference between two terms equals the difference of their indices multiplied by the common difference. Thus, \(a_6-a_3=(6-3)d\). Hence \(25-4=3d\), so \(21=3d\) and \(d=7\). Option 21 is the difference between the given terms, not the common difference. Exam tip: when subtracting two given terms, also use the difference between their subscripts.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
In an AP, the difference between two terms equals the difference of their indices multiplied by the common difference. Thus, \(a_6-a_3=(6-3)d\). Hence \(25-4=3d\), so \(21=3d\) and \(d=7\). Option 21 is the difference between the given terms, not the common difference. Exam tip: when subtracting two given terms, also use the difference between their subscripts.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..
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