Question

If both the sequences $x, a_1, a_2, y$ and $x, b_1, b_2, z$ are in A.P. and it is given that $y > x$ and $z < x$, then which of the following values can $\frac{a_1 - a_2}{b_1 - b_2}$ possibly take?

Accepted Answer

C. In an A.P., $a_1 - a_2 = -d_1$. Since $y > x$, common difference $d_1 > 0$, so $a_1 - a_2 < 0$. For second A.P., $b_1 - b_2 = -d_2$. Since $z < x$, $d_2 < 0$, so $b_1 - b_2 > 0$. Therefore, $\frac{a_1 - a_2}{b_1 - b_2} = \frac{ ext{negative}}{ ext{positive}} < 0$. The only negative option is -3.

Arithmetic Progressions Common Difference Ratio

Explanation

Practise this under exam conditions