Question

If |x|, |x – 1|, |x + 1| are first three terms of an A.P., then sum of it’s first 10 terms is –

• A. 20
• B. 25
• C. 10
• D. 30

Answer 1

Answer: (B)

25

Answer 2

2 |x – 1| = |x + 1| + |x|

$\left\{ \begin{matrix} 2(1 - x) = - x - x - 1 \\ 2(1 - x) = - x + x + 1 \\ 2(1 - x) = x + x + 1 \\ 2(x - 1) = x + x + 1 \end{matrix} \right.\$ $\begin{matrix} x \leq - 1 \

• 1 < x \leq 0 \ 0 < x \leq 1 \ x > 1 \end{matrix}$

̃ x = $\frac{1}{4}$, d = $\frac{1}{2}$

S = 5$\left\lbrack \frac{1}{2} + 9\left( \frac{1}{2} \right) \right\rbrack$ = 25.