# Week 2 – Precalc 11

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 $S_{10}$ for the geometric series 80 + 60 + 45. . .

a = 80

r = 0.75 $S_{10}$ = 80 ( ( $0.75^{10}$ ) – 1) ÷ ( o.75 – 1) $S_{10}$ = 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 $t_n$ = 6561 $t_n$ = a ( $r^{n-1}$

6561 = 3 ( $3^{n-1}$

2187 = ( $3^{n-1}$ $3^7$ $3^{n-1}$

7 = n – 1

8 = n $S_{8}$ = 3 ( $3^8$  – 1 ) ÷  ( 3 – 1) $S_{8}$ = 9840