Q. 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
A) $-1080$
B) $-1020$
C) $-1200$
D) $-120$
Explanation
[Solution by Dr. Abubacker] $S_4=\frac15(S_8-S_4)\Rightarrow S_8=6S_4$. $S_4=12+6d$ and $S_8=24+28d$, so $24+28d=72+36d$ and $d=-6$. $S_{20}=10(6+19d)=10(6-114)=-1080$. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.