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