I want to understand how the formula for the sum of a geometric sequence is created... This is what I understand so far:(adsbygoogle = window.adsbygoogle || []).push({});

A geometric sequence is the sum of a series of numbers, where a term will be multiplied by an amount (the common ratio) to get the next term, and so on... ex: 1+2+4+8...64+128+256

I understand that the first term is 1 and the common ratio is 2...

The formula to find the sum of the series is

SN=a(1-rN)/(1-r)

Where S is the sum for the 'n'th term...

Step by step, they show the formula worked out like this:

1) a + ar^1 + ar^2 + ar^3 + ar^4 ... ar^n-2 + ar^n-1

2) multiply the whole thing by 'r' ... ar + ar^2 + ar^3 + ar^4 ... ar^n-1 + ar^n

3) subtract the two sequences

4) end up with a - ar^n = (1-r) SN

5) rearrange to get SN=a(1-rN)/(1-r)

Okay, so I don't understand anything from 2 down... if you have a sequence in front of you how can you just think "Why don't I just multiply the whole series by its common ratio and subtract it from the first series to find its sum?" ... what's the reasoning behind multiplying it and then cancelling out most of the terms by subtracting? How do you just do something like that out of the blue?

Thanks in advance,

Preet

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# Homework Help: Understanding the formula for a geometric series

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