What is the maximum sum of the terms in the arithmetic progression 25, 241/2, 24............?

• its a decreasing AP 25,24.5,24,23.5,...
  if nth term is zero then
  25 + (n-1)*(-.5) = 0
  => n = 51
  after 51 terms AP contains -ve terms
  so, max sum will be obtained upto 50/51th term
  
  S max = 51/2 *(25+0) = 637.5
  
• 10 years agoHelpfull: Yes(60) No(7)
• It is in a decreasing order as follows 25,24.5,24,23.5,23.......etc.
  As N th term is 0.we know
  an = a+(n-1)*d
  0=25+(n-1)*(-0.5)
  n-1=50
  n= 51.
  and sum of 'n' terms of an AP is given as Sn=n/2*( 2*a + (n-1)*d))
  Sn = 51/2*(25*2+50*(-0.5))
  Sn = 637.5
• 6 years agoHelpfull: Yes(5) No(0)
• maximum sum can be 637.5
• 10 years agoHelpfull: Yes(2) No(3)
• answer is :637.5
• 10 years agoHelpfull: Yes(2) No(3)
• how is second term 24.5 ?
• 9 years agoHelpfull: Yes(0) No(1)