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,…

Bellwork

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

or

Bellwork

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:

Which Formula?

Arithmetic

orDo we know d?

No! S0…

Find the Partial sum of the Arithmetic Series

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

Which Formula?

Arithmetic

orDo we know d?

Yes! S0…

Find the Partial sum of the Arithmetic Series

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

Which Formula?

Arithmetic

orDo we know d?

Yes! S0…

Find the Partial sum of the Arithmetic Series

Plug in what we know and simplify

Oh No! We don’t know n!!!

Let’s Find n!

Now we know n is 25, so we can go back and finish solving!

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

Plug in what we know and simplify

Answer: The partial sum of the geometric sequence is 121.

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