If \(S_u=1431\) and \(S_v=3321\), what is the value of \(u+v\), where \(S_k=1+2+\cdots+k\)?
Answer and explanation
Correct answer: 134
Use \(S_k=\frac{k(k+1)}2\) and identify each given number as a triangular number. For 1431, \(\frac{53\cdot54}{2}=53\cdot27=1431\), so \(u=53\). For 3321, \(\frac{81\cdot82}{2}=81\cdot41=3321\), so \(v=81\). Therefore \(u+v=53+81=134\), which is option A. The other choices would require incorrect indices such as 52 or 82, but direct substitution into the sum formula confirms the two indices uniquely among positive natural numbers.
Frequently asked questions
What is the correct answer to this question?
134
Why is this the correct answer?
Use \(S_k=\frac{k(k+1)}2\) and identify each given number as a triangular number. For 1431, \(\frac{53\cdot54}{2}=53\cdot27=1431\), so \(u=53\). For 3321, \(\frac{81\cdot82}{2}=81\cdot41=3321\), so \(v=81\). Therefore \(u+v=53+81=134\), which is option A. The other choices would require incorrect indices such as 52 or 82, but direct substitution into the sum formula confirms the two indices uniquely among positive natural numbers.
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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