What is the sum of the first (24) terms of the arithmetic progression (10,15,20,\ldots)?
Answer and explanation
Correct answer: 1620
Here, the first term is \(a=10\), the common difference is \(d=5\), and \(n=24\). The 24th term is \(a+(n-1)d=10+23\times5=125\). Therefore, \(S_{24}=\frac{24}{2}(10+125)=12\times135=1620\). Hence, option B is correct. An answer such as \(1632\) can result from using an incorrect last term or number of terms. Exam tip: find the \(n\)th term first and remember to use \((n-1)\).
Frequently asked questions
What is the correct answer to this question?
1620
Why is this the correct answer?
Here, the first term is \(a=10\), the common difference is \(d=5\), and \(n=24\). The 24th term is \(a+(n-1)d=10+23\times5=125\). Therefore, \(S_{24}=\frac{24}{2}(10+125)=12\times135=1620\). Hence, option B is correct. An answer such as \(1632\) can result from using an incorrect last term or number of terms. Exam tip: find the \(n\)th term first and remember to use \((n-1)\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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