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 | 15th 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 | 7th Dec, 2017, 10:11: AM