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Bellwork
Write the Explicit equation for a geometric sequence where a1=-2 and a5=-32
Write a Recursive formula for 4, 1, -2, -5, -8,…
End in Mind
Miranda arranges some rows of dominoes so that after she knocks over the first one, each domino knocks over two more dominoes when it falls. If there are ten rows, how many dominoes does Miranda use?
Vocabulary and Formulas
Series- The result when the terms of a sequence are added together The sum of the first n terms is denoted Sn and is called the partial
sum
Arithmetic Geometric
or or
The process…
Arithmetic or Geometric?
What am I given?
Which Formula do I use?
Plug it all in!... If you don’t have enough information, use what you do know to find what you don’t.
Example 1:Find the Partial sum of the Arithmetic Series
The first term is 14
The 30th term is 101
Givens:
Plug in what we know and simplify
Answer: The sum of the first 30 terms (the partial sum) of this sequence is 1,725.
Example 2:Find the Partial sum of the Arithmetic Series
The first term is 7
We are finding the sum of the first 10 terms
Givens:
The common difference is 8
Plug in what we know and simplify
Answer: The sum of the first 10 terms (the partial sum) of this sequence is 430.
Example 3:Find the Partial sum of the Arithmetic Series
The first term is 12
The last term of the ones we’re adding together is 180
Givens:
The common difference is 7
Plug in what we know and simplify
Answer: The partial sum is 2400 We found n! It’s 25!
Oh No! We don’t know n!!!
Example 4:Find the Partial sum of the Geometric Series
The first term is 16
The common ratio is 2
Givens:
We are finding the sum of the first 8 terms
Which Formula?
Which Formula uses what we’re given???
Geometric
or
We’re given n, not an
Find the Partial sum of the Geometric Series
Plug in what we know and simplify
Answer: The sum of the first 8 terms of the sequence (the partial sum) is 4,080
Example 5:Find the Partial sum of the Geometric Series
The first term is 1
The common ratio is 3
Givens:
The last term of the ones we’re adding together is 81
Which Formula?
Which Formula uses what we’re given???
Geometric
or
We’re given an not n
Find the Partial sum of the Geometric Series
Partial Sum Practice:
1) Find the partial sum of the arithmetic sequence where a1=-3 and a8=32
2) Find the partial sum of the geometric sequence where a1=2, an=2048, and r=4
3) Find the partial sum of the arithmetic sequence 9, 14, 19, 24,…59
4) Find the partial sum of the geometric sequence where a1=4, r=5, and n=6
5) Find the partial sum of the arithmetic sequence where a1=15, n=10, and d=-2