Question 70

# If both the sequences x, a1, a2, y and x, b1, b2, z are in A.P. and it is given that $$y > x$$ and $$z < x$$, then which of the following values can $$\left\{\frac{(a1-a2)}{(b1-b2)}\right\}$$ possibly take?

Solution

The two given sequences in AP are :

x, a1, a2, y and x, b1, b2, z.

Additionally, it is given that : y  > x and z < x.

Hence the common difference is not zero for both the series :

Since y > x the common difference is positive for the first series. (Considering the common difference to be d1)

Similarly z < x the common difference is negative for the given series. (Considering the common difference to be d2)

Now for the given value :

$$\frac{\left(a1-a2\right)}{\left(b1-b2\right)}$$

The value of a1 - a2 is negative and b1 - b2 is positive.

Hence the value of $$\frac{\left(a1-a2\right)}{\left(b1-b2\right)}$$ takes a negative value.

The only possible option is -3.

The answer is option C.

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