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

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-1020

-1200

-120

-1080

answer is B.

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Detailed Solution

$\begin{array}{l} a = 3 \\ S_{4} = \frac{1}{5} (S_{8} - S_{4}) \\ \Rightarrow 5 S_{4} = S_{8} - S_{4} \\ \Rightarrow 6 S_{4} = S_{8} \\ \Rightarrow 6 \cdot \frac{4}{2} [2 \times 3 + (4 - 1) \times d] \\ = \frac{8}{2} [2 \times 3 + (8 - 1) d] \\ \Rightarrow 12 (6 + 3 d) = 4 (6 + 7 d) \\ \Rightarrow 18 + 9 d = 6 + 7 d \\ \Rightarrow d = - 6 \\ S_{20} = \frac{20}{2} [2 \times 3 + (20 - 1) (- 6)] \\ = 10 [6 - 114] \\ = - 1080 \end{array}$

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