PUMPA - SMART LEARNING

எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

Book Free Demo
1. The sum of first \(n\), \(2n\) and \(3n\) terms of an A.P are \(S_1\), \(S_2\) and \(S_3\) respectively. Prove that \(S_3 = 3(S_2 - S_1)\).
 
 
2. The sum of first \(n\) terms of a certain series is given as \(2n^2 - 3n\). Show that the series is an A.P.
 
 
3. If \(S_1\), \(S_2\), \(S_3\), …, \(S_m\) are the sums of \(n\) terms of \(m\) A.P.'s whose first terms are \(1, 2, 3, … m\) and whose common differences are \(1, 3, 5, …, (2m - 1)\) respectively, then show that S1+S2+S3+...+Sm=12mnmn+1.
 
Important!
This is a self-assessment task. Solve this question and assess the solution steps after the test's completion on your own.