1. 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,…

2. Bellwork
Write the explicit expression for a geometric sequence where a1=-2 and a5=-32 or

3. Bellwork
Write a Recursive formula for 4, 1, -2, -5, -8,…

4. 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?

5. 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

6. 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.

7. Example 1: Find the Partial sum of the Arithmetic Series
Givens:
The first term is 14
The 30th term is 101

8. Which Formula? No! S0… Do we know d? Arithmetic
Find the Partial sum of the Arithmetic Series
Which Formula?
Arithmetic
Do we know d? or
No! S0…

9. Plug in what we know and simplify
Answer: The sum of the first 30 terms (the partial sum) of this sequence is 1,725.

10. Example 2: Find the Partial sum of the Arithmetic Series
Givens:
The first term is 7
We are finding the sum of the first 10 terms
The common difference is 8

11. Which Formula? Do we know d? Yes! S0… Arithmetic
Find the Partial sum of the Arithmetic Series
Which Formula?
Arithmetic
Do we know d? or
Yes! S0…

12. Plug in what we know and simplify
Answer: The sum of the first 10 terms (the partial sum) of this sequence is 430.

13. Example 3: Find the Partial sum of the Arithmetic Series
Givens:
The first term is 12
The last term of the ones we’re adding together is 180
The common difference is 7

14. Which Formula? Do we know d? Arithmetic Yes! S0…
Find the Partial sum of the Arithmetic Series
Which Formula?
Arithmetic
Do we know d? or
Yes! S0…

15. Plug in what we know and simplify
Oh No! We don’t know n!!!

16. Let’s Find n! Now we know n is 25,
so we can go back and finish solving!

17. Plug in what we know and simplify
Oh No! We don’t know n!!!
We found n! It’s 25!
Answer: The partial sum is 2400

18. Example 4: Find the Partial sum of the Geometric Series
Givens:
The first term is 16
The common ratio is 2
We are finding the sum of the first 8 terms

19. Which Formula? Which Formula uses what we’re given??? Geometric
Find the Partial sum of the Geometric Series
Which Formula?
Geometric
Which Formula uses
what we’re given??? or
We’re given n, not an

20. Plug in what we know and simplify
Answer: The sum of the first 8 terms of the
sequence (the partial sum) is 4,080

21. Example 5: Find the Partial sum of the Geometric Series
Givens:
The first term is 1
The last term of the ones we’re adding together is 81
The common ratio is 3

22. Which Formula? Which Formula uses what we’re given??? Geometric
Find the Partial sum of the Geometric Series
Geometric
Which Formula uses
what we’re given??? or
We’re given an not n

23. Plug in what we know and simplify
Answer: The partial sum of the
geometric sequence is 121.

24. Partial Sum Practice:
Find the partial sum of the arithmetic sequence where a1=-3 and a8=32
Find the partial sum of the geometric sequence where a1=2, an=2048, and r=4
Find the partial sum of the arithmetic sequence 9, 14, 19, 24,…59
Find the partial sum of the geometric sequence where a1=4, r=5, and n=6
Find the partial sum of the arithmetic sequence where a1=15, n=10, and d=-2