If m times the mth series of an A.P. is equal to n times its nth series, what is the (m+n)th term of the A.P. ? Choose one:
A) 1  B) m  C) n  D) 0  E) 2
mth term of an A.P.   Am = a + (m-1)d   nth term of an A.P.   An = a + (n+1)d   [here a= First term of an A.P   d= difference between two consecutive terms   Am= mth term of A.P.]   According to the question;   m*Am = n*An   m(a + (m-1)d)= n(a + (n-1)d)   m(a + md - d)= n(a + nd - d)   am + m^2d-md = an + n^2d - nd   a(m-n)+ (m^2-n^2)d -(m-n)d = 0   a(m-n)+ (m-n)(m+n)d -(m-n)d= 0   (m-n)[a + (m+n)d - d ]= 0   [a + (m+n)d - d ]= 0   [a + (m+n-1)d ]= 0   So Am+n = 0   so answer will be 0   ANSWER:0
<result>D</result>
If m times the mth series of an A.P. is equal to n times its nth series, what is the (m+n)th term of the A.P. ?