Arithmetic and Geometric Progressions

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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

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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



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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.