How to find the general term for the first 'n' terms of a geometric series

Here I'll be demonstrating how to find the general term for the first 'n' terms of a geometric series:

Definitions:

a = First term

r = The common ratio

Step 1:

S_n = a + ar + ar^2 + ar^3 + ... + ar^(n-2) + ar^(n-1)

Step 2:

rS_n = ar + ar^2 + ar^3 + ar^4 + ... + ar^(n-1) + ar^n

Step 3:

S_n - rS_n = a - ar^(n)

Step 4:

S_n(1-r) = a(1-r^n)

Step 5:

S_n = [a(1-r^n)]/(1-r)

Video:

You can watch the video below to see the workings in more detail...

• Article by Tiago Hands: https://www.instagram.com/tiago_hands

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• Lead image: By Gitti Lohr from Pixabay