Q. 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. ?
Option
A) 1
B) m
C) n
D) 0

• 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
  
  
• 10 years agoHelpfull: Yes(36) No(2)