Find the common difference of an AP whose first term is 100 and sum of whose first 6

terms is 5 times the sum of next 6 terms.

We have to find common difference d .

Here first term a = 100

S₆= $\frac{n}{2}$ {2a +{n-1}d

S₆ =3{2{100}+{6-1}d

S₆=3{200+5d}

S₆=600+15d

now, S₁₂=$\frac{12}{2}${200 +11d}

 S₁₂-S₆ =1200+66d -600-15d

So  next 6 term =600 +51d

 According to question

  600+15d = 5{600+51d}

 600+15d=3000 +255d

 255d -15d =600 -3000

 240d= -2400

 d = -2400/240

 d = -10