The sum of 5 numbers in AP is 30 and the sum of their squares is 190. Which of the following is the third term?

• consider the 5 numbers in AP as a-2d,a-d,a,a+d,a+2d;
  given,a-2d+a-d+a+a+d+a+2d=30;
  5a=30==>a=6
  here a is the 3 rd term so..third term is 6..
• 8 years agoHelpfull: Yes(31) No(1)
• a is first number d is common diff.
  (5/2)(2a+4d)=30
  implies a+2d=6
  which is the third term so answer is 6
  
• 8 years agoHelpfull: Yes(6) No(0)
• s5=30
  sn=avg*n
  avg=sn/n=s5/5=30/5=6
  1st 2nd 3rd 4th 5th
  Avg of 1st,5th = avg of 2nd, 4th = 3rd = avg = 6
  so 3rd term is 6.
• 8 years agoHelpfull: Yes(2) No(0)
• (a+-2d)+(a-d)+a+(a+d)+(a+2d)=30
  5a=30
  a=6
  which is the third term
• 8 years agoHelpfull: Yes(2) No(0)
• 6
  
  For first term=a and difference=d of an AP, Sum=(5/2)[2*a+4*d]=30, a+2d=6
  Possible combinations of (a,d) are (4,1), (2,2), (0,3)
  So the series can be 4,5,6,7,8 or 2,4,6,8,10 or 0,3,6,9,12
  With the given condition of sum of squares to be 190, the series is 4,5,6,7,8 with third term=6
• 8 years agoHelpfull: Yes(0) No(0)
• 5a=30 then a=6
• 8 years agoHelpfull: Yes(0) No(0)
• 5a-=30-->a=6
• 7 years agoHelpfull: Yes(0) No(0)