What is the sum of the first (16) terms of the AP (24,30,36,\ldots)?
Answer and explanation
Correct answer: 1104
Here, the first term is \(a=24\), the common difference is \(d=30-24=6\), and \(n=16\). The 16th term is \(a_{16}=a+(16-1)d=24+15\times6=114\). Thus, \(S_{16}=\frac{16}{2}(24+114)=8\times138=1104\). Therefore, 1104 is correct. An option such as 1094 can result from an error in addition or multiplication. Exam tip: You can also apply \(S_n=\frac{n}{2}[2a+(n-1)d]\) directly.
Frequently asked questions
What is the correct answer to this question?
1104
Why is this the correct answer?
Here, the first term is \(a=24\), the common difference is \(d=30-24=6\), and \(n=16\). The 16th term is \(a_{16}=a+(16-1)d=24+15\times6=114\). Thus, \(S_{16}=\frac{16}{2}(24+114)=8\times138=1104\). Therefore, 1104 is correct. An option such as 1094 can result from an error in addition or multiplication. Exam tip: You can also apply \(S_n=\frac{n}{2}[2a+(n-1)d]\) directly.
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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