Median is the first term => Common ratio has to be negative. why?
Let us see why this is true.
When a > 0,
If r > 1, this will be an increasing G.P.
If r lies between (0, 1), this will be a decreasing G.P.
In both cases, the middle term will be the median. If a < 0, the order will be the other way around, but the middle term would still be the median.
If the middle term is not the median, we can say that r < 0. Now, let us go the solution
b = 10, a and c should be negative. Solution, a + b + c cannot be 15.
a + b + c = –15
Solving the quadratic, we will get r = or -2.
The sequence is either – 5, 10, – 20 or – 20, 10, – 5.
a > c => the sequence has to be – 5, 10, – 20.
The product of the first 4 terms = – 5 × 10 × –20 × 40 = 40000.
Correct Answer: 40000