If (S_n=2485), what is the value of (S_n-S_{n-5})?
Answer and explanation
Correct answer: 340
Here, \(S_n\) denotes the sum of the first \(n\) natural numbers. From \(\frac{n(n+1)}{2}=2485\), we get \(n=70\), since \(\frac{70\times71}{2}=2485\). Therefore, \(S_n-S_{n-5}=S_{70}-S_{65}\), which is the sum of the last five numbers: \(66,67,68,69,70\). Hence, \(66+67+68+69+70=340\). Choosing 350 would miss the correct first term, 66, among these five terms. Exam tip: \(S_n-S_{n-r}\) always represents the sum of the last \(r\) terms.
Frequently asked questions
What is the correct answer to this question?
340
Why is this the correct answer?
Here, \(S_n\) denotes the sum of the first \(n\) natural numbers. From \(\frac{n(n+1)}{2}=2485\), we get \(n=70\), since \(\frac{70\times71}{2}=2485\). Therefore, \(S_n-S_{n-5}=S_{70}-S_{65}\), which is the sum of the last five numbers: \(66,67,68,69,70\). Hence, \(66+67+68+69+70=340\). Choosing 350 would miss the correct first term, 66, among these five terms. Exam tip: \(S_n-S_{n-r}\) always represents the sum of the last \(r\) terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
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