Geometric Series

Hi Everyone, this is Vivian blogging again!! I am going to be explaining Geometric Series.

Series:
1.) The series of a geometric sequence is the sum of certain number of terms in the sequence or the sum of all of the terms in the sequence.

2.) To find the sum of n terms in a geometric sequence use the formula:
Sn = t1 (1-r^n) / 1-r

Sigma Notation:
1.) Is an alternate notation for finding geometric series (the sum)

2.) Sigma means the sum of all terms in a sequence.

Formulas for Geometric Sequences:
1.) Common Ration r = t2/t1 Note: r = t2/t1 = t3/t2 = t4/t3 = t5/t4, etc.

2.) To find a specific term use the formula: tn = t1 x r^n-1

3.) To find one geometric mean use: +- √ (t1)(t3)

4.) When finding more than one geometric mean use tn = t1 x r^n-1 to find the common ratio and then multiply to find the missing terms.

Example 1:
Given the geometric sequence 2,6,18........find the sum of the first ten terms.

1.) First thing is you list out what you know.
t1 = 2
r = 6/2 = 3

2.) Then you solve for S10, so you use the formula Sn = t1 (1-r^n) / 1-r.

3.) You then plug in the numbers into your formula so:
S10 = 2 (1-3^10)/1-3

4.) After calculating this out your answer for S10 = 59048.

Example 2:
Find the sum of the first fifteen terms for a geometric sequence whose first term is 4920 and whose common ratio is 1/2.

1.) List out what you know:
t1 = 4820, r = 1/2

2.) You're solving for the sum of the first fifteen terms so the formula is Sn = t1 (1-r^n) / 1-r.

3.) Plug your numbers into the formula:
S15 = 4820 (1 - 1/2^15) / 1-1/2

4.) S15 = 9638.705811.

Hope this helped at least one person! I'm not good at blogging so I don't have pictures. Bye!! Have a nice day :)