The 12th term of an arithmetic series is 42 and the sum of the first 17 terms is 51. Find the common difference of the series, and find the first three terms of the series.

• Common difference=13 & first three terms are -101, -88, -75
  
  If the first term=a and common difference=d, then
  12th term of arithmetic series=a+11*d=42 ---(i) &
  Sum of first 17 terms=(17/2)[2a+16*d]=51 or 34a+374d=1428 ---(ii)
  From (i) & (ii), d=13, a=-101
  So first three terms are -101, (-101+13=-88), (-88+13=-75)
• 9 years agoHelpfull: Yes(0) No(0)
• 12 th term= a+11d=42 -------2
  sum of first 17 numbers= (17/2)(2a+16d)=51
  2a+16d=6
  a+8d=3 -------1
  solving 1 & 2 we get d=13 a =-101
  first three terms are -101 -88 -75
  
• 9 years agoHelpfull: Yes(0) No(0)