Geometric progression

Hi Siva,

Can you post a link to the original prompt? I think that something might be 'off' with the formatting in the question.

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

Please find the q.no 4 in the below link:
new-tough-and-tricky-exponents-and-roots-questions-125956.html

Thanks
Siva

Hi Siva,

The question that you posted did not properly display the exponents involved, so I've transcribed it here:

What is the value of 5 + 4(5) + 4(5^2) + 4(5^3) + 4(5^4) + 4(5^5)?

5^6
5^7
5^8
5^9
5^10

This question can be solved in a number of different ways. Looking at the answer choices, we know that some 'power of 5' WILL be the sum, so thinking in those terms should help. There's actually a great 'pattern matching' shortcut in this question that you can use to avoid much of the 'math' involved.

First, let's look at the first two terms in the calculation:

5 + 4(5)
5 + 20 = 25
25 = 5^2

That's interesting that the first two terms, when added together, give us a 'power of 5'.....

What happens when we add the next term....

5 + 4(5) + 4(5^2)
5 + 20 + 100 = 125
125 = 5^3

Now things are getting REALLY interesting....adding the third term made the sum equal the 'next power of 5'.....

I wonder if that pattern continues.....

5 + 4(5) + 4(5^2) + 4(5^3)
5 + 20 + 100 + 500 = 625
625 = 5^4

This is clearly a pattern. Calculating the last two pieces of the sum are unnecessary. With each additional 'piece', we end up increasing the 'power of 5' by "1".....There are two more pieces, so there are two more 'powers of 5'

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Thanks Rich for the fabulous explanation.

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