Sir, in fact I have not understood the question at all. According to me the som of n termes of two different AP's can be same iff a=A a.d d=D as per your final equation in spite of only one value of n. I would request you to please give a practical example of the above question satisfying the last equation as above to understand the meaning properly.
 

Asked by sudhanshubhushanroy | 16th Nov, 2017, 02:12: PM

Expert Answer:

begin mathsize 16px style 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight d equals 2 straight b plus left parenthesis straight n minus 1 right parenthesis straight D
the space above space equation space is space just space showing space that
the space terms space of space AP space are space same space
straight t equals straight a plus left parenthesis straight n minus 1 right parenthesis straight d
so space by space putting space straight n subscript 1 comma straight n subscript 2..... end subscript space space we space will space get space equal space terms space on space both space sides space
so space their space sum space will space be space equal space too space upto space same space straight n.
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Answered by Arun | 18th Nov, 2017, 08:40: AM