If the first term of an AP is 2 and the sum of the first five terms...

If the first term of an AP is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, then what is the sum of the first ten terms?

Options

A $-500$
B $-250$
C $500$
D $250$

Correct answer

B. $-250$

Step-by-step solution

Let common difference

=d

. Then, sum of first 5 terms

=\frac{\text{ Sum of next } 5 \text{ terms }}{4}

\begin{aligned} & \Rightarrow \frac{1}{2} \cdot 5(4+4 \cdot d)=\frac{1}{4} \cdot \frac{1}{2} \cdot 5\{(2+5 \cdot d)+4 \cdot d\} \\ & \Rightarrow 4 \times 4(1+d)=4+14 d\end{aligned}

\therefore d=-6 \text{. }\therefore

Sum of first ten terms=

\frac{1}{2} \times10\{(2 \times2+9(-6)\}=-250.

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