JEE Mains · Maths · STD 11 - 8. sequence and series
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 \(-120\)
Answer & Solution
Correct Answer
(A) \(-1080\)
Step-by-step Solution
Detailed explanation
\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}]…
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