If (a_7=36) and (a_{16}=90), what is the common difference of the AP?
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. Thus, \(a_{16}-a_7=(16-7)d\). Hence, \(90-36=9d\), so \(d=6\). If the difference were 7, the difference across 9 positions would be \(63\), not the given \(54\). Exam tip: When two terms of an AP are known, use \(d=\frac{a_n-a_m}{n-m}\) directly.
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. Thus, \(a_{16}-a_7=(16-7)d\). Hence, \(90-36=9d\), so \(d=6\). If the difference were 7, the difference across 9 positions would be \(63\), not the given \(54\). Exam tip: When two terms of an AP are known, use \(d=\frac{a_n-a_m}{n-m}\) directly.
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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