Arithmetic and Geometric Progressions

You are here: Home  CAT Questionbank   CAT Quant  AP, GP  Question 6

GP Median

    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.?
    1. 40000
    2. 32000
    3. 8000
    4. 48000


  • Correct Answer
    Choice A. 40000

Explanatory Answer

Click to watch video solution
Click to view the explanation as a slide show

Detailed Solution

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

Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play

More questions from Progressions

  1. Counting and Progressions
  2. Common Ratio
  3. Common Difference
  4. Sum up to 'n' Terms
  5. AP Puzzle
  6. GP Logical Puzzle
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. Reinforce these ideas with these questions.