Alg 2 Ch 12 Part 5 Geometric Series

Alg 2 Ch 12 Part 5 Geometric Series

By Andi Palodichuk

GEOMETRIC SERIES

The sum of the terms in a geometric sequence.

​Find the sum of the 1st 12 terms of 3, -9, 27, -81, ...

​Here is the formula to find the SUM of a geometric sequence

S_n = the sum
a₁ = first term
r = ratio
n = # of terms you want the sum of

​a1 = 3
r = -3
n = 12

​= -398580

Multiple Choice

Find the sum of the first 8 terms of the geometric series below:
-1 -3 -9 - 27...,

• -3280
• -3135
• -3323
• -3343

Multiple Choice

What is the sum of the first ten terms of the sequence 4, -12, 36, -144 . . . ?

• 59,050
• -59,048
• -78,732
• 118,096

Multiple Choice

Find the indicated sum for the geometric series.
S₆ for (-4/5) + 8 + (-80) + 800 + ....

• _S6 = 21,845
• _S6 = 72,000
• _S6 = 72,727.2
• _S6 = -128,840.8

The Greek Letter meaning summation or sum of ​

​

We also use this symbol for Geometric Sequence

​

NOTE: Formula for terms is whatever function we use. ​Depending on the problem.

​

What does the Sigma notation mean? ​

​

​So this means plug in 1 to the expression 3x
Then plug in 2, then 3, then 4, then 5. Stop at 5 and add up your answers

Multiple Choice

Find the sum

• 25

• 36

• 15

• 55

• 62

Multiple Choice

Find the sum

• 58

• 40

• 32

• 10

• 37

3(4)^n-1 Looks like our Geometric Sequence formula so we would know that
a₁ = 3
r = 4
and n = 8 (that's on top of the Σ)

So we can use this formula to find the sum instead of plugging in 1, 2, 3, 4, 5, 6, 7, 8.

​= 65535

Multiple Choice

$$Evaluate\ \ \ \ \ \sum_{x=1}^9-3\cdot3^{\ \left(x-1\right)}$$  

• -28,056

• -29,523

• -31,724

• -30,628

Multiple Choice

Evaluate  $$\sum_{k\ =\ 1}^71\left(-2\right)^{k\ -1\ }$$  

• 44

• $$\frac{1}{3}$$  

• 43

• 49

Multiple Choice

Find the sum of the finite geometric series:

• 88419

• 78124

• 91846

• 92234

Multiple Choice

Write the following series in sigma notation for the first 6 terms. 

• $$\sum_{k=1}^6-81\left(-\frac{2}{3}\right)^{k-1}$$  

• $$\sum_{k=1}^5-81\left(-\frac{2}{3}\right)^{\left(k-1\right)}$$  

• $$\sum_{k=0}^6-81\left(-\frac{2}{3}\right)^k$$