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. ?
Options
A) 0
B) m
C) n
D) mn
E) None of these
Explanation :   Here's the solution :   mth term of an A.P.   Am = a + (m-1)d-------------------------------(1)   nth term of an A.P.   0n = a + (n+1)d--------------------------------(2)   [Here a= First term of an 0.P   d= difference between two consecutive terms ]   Now , 0ccording to the question;   m*0m = n*0n   m(a + (m-1)d)= n(a + (n-1)d)   m(a + md - d)= n(a + nd - d)   am + m2d-md = an + n2d - nd   a(m-n)+ (m2-n2)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-------------------------------------(3)   Hence , 0ccording to equation (3)   0m+n = 0   Hence (0) is the correct answer   0nswer : 0
<result>A</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. ?