CBSE Class 11-science Answered

Prove that the sum of n numbers of terms of two different AP's can be same for only one value of n.

Asked by sudhanshubhushanroy | 15 Nov, 2017, 08:37: PM

Expert Answer

begin mathsize 16px style Let space straight a comma space straight a plus straight d comma space straight a plus 2 straight d comma...... then space straight S subscript straight n equals straight n over 2 open square brackets 2 straight a plus open parentheses straight n minus 1 close parentheses straight d close square brackets Let space straight b comma space straight b plus straight D comma space straight b plus 2 straight D comma..... then space straight S subscript straight n space equals straight n over 2 open square brackets 2 straight b plus open parentheses straight n minus 1 close parentheses straight D close square brackets Consider comma straight n over 2 open square brackets 2 straight a plus open parentheses straight n minus 1 close parentheses straight d close square brackets equals straight n over 2 open square brackets 2 straight b plus open parentheses straight n minus 1 close parentheses straight D close square brackets 2 straight a plus open parentheses straight n minus 1 close parentheses straight d equals 2 straight b plus open parentheses straight n minus 1 close parentheses straight D Hence comma space sum space of space straight n space numbers space of space terms space of space two space different space Ap apostrophe straight s space can space be space same space for space the space only one space value space of space straight n. end style

Answered by Sneha shidid | 07 Dec, 2017, 10:11: AM

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