This week in precalc 11 we learned about geometric series.

Geometric series is the sum of the terms of a geometric sequences, a series with a constant ratio between successive terms. For example, a geometric series would be 6 + 12 + 24 + 48 + . . . The common ratio is the ratio between two numbers in a geometric sequence. To determine the common ratio, you can just divide each number from the number preceding it in the sequence (formula: r = a(n) / a(n – 1) ).

We also learned how the formula for determining the sum of the first n terms in any geometric series using the formula: 

Here’s an example on how to apply this

↓

Find for the geometric series 80 + 60 + 45. . .

a = 80

r = 0.75

= 80 ( ( ) – 1) ÷ ( o.75 – 1)

= 301.98

Another example       ↓

For the geometric series 3, 9, 27. . . 6561, determine how many terms it has and then calculate its sum.

r = 3

a = 3

= 6561

= a (

6561 = 3 ( 

2187 = (

= 

7 = n – 1

8 = n

= 3 (   – 1 ) ÷  ( 3 – 1)

= 9840