The question is about Product of terms in A Geometric Progression. When the median of three terms is one of the terms, how we can find out the product of the terms? With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. CAT Exam tests the idea of progression often in the CAT Quantitative Aptitude section and this could also be tested in DI LR section of the CAT Exam as a part of a puzzle.

Question 6: Consider a, b, c in a G.P. such that |a + b + c| = 15. The median of these three terms is a, and b = 10. If a > c, what is the product of the first 4 terms of this G.P.?

- 40000
- 32000
- 8000
- 48000

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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

\\frac{ 10 }{r}\\) + 10 + 10r = -15 \\Rightarrow\\) \\frac{2}{r}\\) + 2r = -5

Solving the quadratic, we will get r = \\frac{-1}{2}\\) 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.

The question is **"what is the product of the first 4 terms of this G.P.?"**

Choice A is the correct answer.

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