Geometric progression

Question

Hi Maths experts, Can any one clear my doubt? When I'm preparing few problems, I have come across a geometric progression sum. But I don't know which is the correct formula to use and what's the difference.? Below they are given. Please let me know which formula to use on what occasion Formula 1: Sn: a∗(r^n−1)/r−1 Where a =1st term; r = difference; n=number of terms Formula 2: Sn: a*(1-r^n)/1-r Where a =1st term; r = difference; n=number of terms During my school days, my maths teacher had tough time taught me progression sums and that follows here

(Just kidding

) Your help is much appreciated. Thanks

EMPOWERgmatRichC · Answer

Hi SivaKumarP,

On the GMAT, these types of 'sequence notation' questions are relatively rare (you'll likely see just one). In addition, you're typically given the equation for the sequence, so most of the 'work' that you have to do is based on figuring out how the sequence progresses and what pattern(s) exist within it. In that way, having these types of sequence "formulas" memorized isn't necessary.

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

SivaKumarP · Answer

Hi EMPOWERgmatRichC,

Thanks for the info.

However I asked this doubt for some other type problem.

4. What is the value of 5+4∗5+4∗52+4∗53+4∗54+4∗55?
A. 5^6
B. 5^7
C. 5^8
D. 5^9
E. 5^10

This above problem has been solved using the geometric progression in one of the gmat club forum, so thought clarifying that doubt..

Thanks
Siva

EMPOWERgmatRichC · Answer

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

SivaKumarP · Answer

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

EMPOWERgmatRichC · Answer

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:  5^6

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

SivaKumarP · Answer

Thanks Rich for the fabulous explanation.

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Geometric progression

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