What is the sum of the first (9) terms of the AP (6,11,16,\ldots)?
Answer and explanation
Correct answer: 234
Here, \(a=6\), \(d=11-6=5\), and \(n=9\). The ninth term is \(a_9=a+(n-1)d=6+8\times5=46\). Hence, \(S_9=\frac{n}{2}(a+a_9)=\frac{9}{2}(6+46)=234\). Therefore, 234 is the correct answer. A result such as 238 can occur if the last term or the number of terms is taken incorrectly. Exam tip: write down \(a\), \(d\), and \(n\) before using the AP sum formula.
Frequently asked questions
What is the correct answer to this question?
234
Why is this the correct answer?
Here, \(a=6\), \(d=11-6=5\), and \(n=9\). The ninth term is \(a_9=a+(n-1)d=6+8\times5=46\). Hence, \(S_9=\frac{n}{2}(a+a_9)=\frac{9}{2}(6+46)=234\). Therefore, 234 is the correct answer. A result such as 238 can occur if the last term or the number of terms is taken incorrectly. Exam tip: write down \(a\), \(d\), and \(n\) before using the AP sum formula.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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