If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

Step-by-step solution

aligned & a =3 & ~S ₄= 1 5 ( ~S ₈- S ₄ ) & 5 ~S ₄= S ₈- S ₄ & 6 ~S ₄= S ₈ & 6 4 2 [2 3+(4-1) d ] & = 8 2 [2 3+(8-1) d ] & 12(6+3 ~d )=4(6+7 ~d ) & 18+9 ~d =6+7 ~d & ~d =-6 & ~S ₂₀= 20 2 [2 3+(20-1)(-6)] & =10[6-114] & =-1080 aligned