If the first term of an AP is (9) and (a_{21}=69), what is (d)?
Answer and explanation
Correct answer: 3
The nth-term formula of an AP is \(a_n=a+(n-1)d\). Here, \(a=9\) and \(a_{21}=69\), so \(69=9+(21-1)d=9+20d\). Hence, \(20d=60\), giving \(d=3\). If 2 were used, the 21st term would be \(9+20\times2=49\), not 69. Exam tip: the nth term contains \((n-1)d\), not \(nd\).
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The nth-term formula of an AP is \(a_n=a+(n-1)d\). Here, \(a=9\) and \(a_{21}=69\), so \(69=9+(21-1)d=9+20d\). Hence, \(20d=60\), giving \(d=3\). If 2 were used, the 21st term would be \(9+20\times2=49\), not 69. Exam tip: the nth term contains \((n-1)d\), not \(nd\).
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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