If the (31)st term of the AP (v-12,v-3,v+6,\ldots) is (438), what is the value of (v)?
Answer and explanation
Correct answer: 180
The difference between consecutive terms is \((v-3)-(v-12)=9\), so \(d=9\) and the first term is \(a=v-12\). The nth term is \(a_n=a+(n-1)d\). Hence, \(438=(v-12)+30\times9=v+258\), giving \(v=180\). If \(v=176\), the 31st term would be \(434\), so it is not correct. Exam tip: In an AP, multiply the common difference by \(n-1\), not by \(n\).
Frequently asked questions
What is the correct answer to this question?
180
Why is this the correct answer?
The difference between consecutive terms is \((v-3)-(v-12)=9\), so \(d=9\) and the first term is \(a=v-12\). The nth term is \(a_n=a+(n-1)d\). Hence, \(438=(v-12)+30\times9=v+258\), giving \(v=180\). If \(v=176\), the 31st term would be \(434\), so it is not correct. Exam tip: In an AP, multiply the common difference by \(n-1\), not by \(n\).
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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