What is the sum of the first (22) terms of the AP (32,36,40,\ldots)?
Answer and explanation
Correct answer: 1628
Here, the first term is \(a=32\), the common difference is \(d=4\), and the number of terms is \(n=22\). The 22nd term is \(a_{22}=32+(22-1)\times4=116\). Hence, \(S_{22}=\frac{22}{2}(32+116)=11\times148=1628\). Therefore, option C is correct. A value such as 1616 may result from using an incorrect last term or mishandling \(n-1\). In an exam, identify \(a\), \(d\), and \(n\) before applying \(S_n=\frac{n}{2}[2a+(n-1)d]\).
Frequently asked questions
What is the correct answer to this question?
1628
Why is this the correct answer?
Here, the first term is \(a=32\), the common difference is \(d=4\), and the number of terms is \(n=22\). The 22nd term is \(a_{22}=32+(22-1)\times4=116\). Hence, \(S_{22}=\frac{22}{2}(32+116)=11\times148=1628\). Therefore, option C is correct. A value such as 1616 may result from using an incorrect last term or mishandling \(n-1\). In an exam, identify \(a\), \(d\), and \(n\) before applying \(S_n=\frac{n}{2}[2a+(n-1)d]\).
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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