Verified Solution • 2025–26 Session moderate QJEEM25Maaf2c: JEE Main 2025 Mathematics - Class 11 JEEM25Maaf2c Solution: If the first term of an A.P. is 3 and the sum of its first four … 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 Multiple Choice Options A −120-120−120 B −1200-1200−1200 C −1080-1080−1080 D −1020-1020−1020 Step-by-Step Verified Solution amp;a=3amp; S4=15( S8−S4)amp;⇒5 S4=S8−S4amp;⇒6 S4=S8amp;⇒6⋅42[2×3+(4−1)×d]amp;=82[2×3+(8−1)d]amp;⇒12(6+3 d)=4(6+7 d)amp;⇒18+9 d=6+7 damp;⇒ d=−6amp; S20=202[2×3+(20−1)(−6)]amp;=10[6−114]amp;=−1080\begin{aligned}& \mathrm{a}=3 \\& \mathrm{~S}_4=\frac{1}{5}\left(\mathrm{~S}_8-\mathrm{S}_4\right) \\& \Rightarrow 5 \mathrm{~S}_4=\mathrm{S}_8-\mathrm{S}_4 \\& \Rightarrow 6 \mathrm{~S}_4=\mathrm{S}_8 \\& \Rightarrow 6 \cdot \frac{4}{2}[2 \times 3+(4-1) \times \mathrm{d}] \\& =\frac{8}{2}[2 \times 3+(8-1) \mathrm{d}] \\& \Rightarrow 12(6+3 \mathrm{~d})=4(6+7 \mathrm{~d}) \\& \Rightarrow 18+9 \mathrm{~d}=6+7 \mathrm{~d} \\& \Rightarrow \mathrm{~d}=-6 \\& \mathrm{~S}_{20}=\frac{20}{2}[2 \times 3+(20-1)(-6)] \\& =10[6-114] \\& =-1080\end{aligned}amp;a=3amp; S4=51( S8−S4)amp;⇒5 S4=S8−S4amp;⇒6 S4=S8amp;⇒6⋅24[2×3+(4−1)×d]amp;=28[2×3+(8−1)d]amp;⇒12(6+3 d)=4(6+7 d)amp;⇒18+9 d=6+7 damp;⇒ d=−6amp; S20=220[2×3+(20−1)(−6)]amp;=10[6−114]amp;=−1080 Related Learning Resources & Exam Preparation JEE Main PYQ Question Bank Browse year-wise authentic previous years' questions with solutions Authentic CBT Mock Tests Simulate official exam environment with live timer and percentile scoring