Unit 5 Sequences

Question 1

finite

The formula for the nth term of an arithmetic sequence is given by.

an=

Answer 1

nth aka explicit form

Question 2

Finite

The formula for the nth term of an geometric sequence is given by.

an=

Answer 2

nth aka explicit form

Question 3

To find a formula for an for the nth term (explicit) of the arthmetic sequence, what would the common difference be?

Answer 3

The common difference would be 4.

notes

Question 4

Explain what each are?

Answer 4

1. The geometric sequence given in recurrence form. Ratio = 10
2. The formula for the explicit form aka “nth term formula”

geometrics deal with ratio (division) and multiplication

Question 5

To find a formula for an for the nth term of the geometric sequence, what would the common difference be?

Answer 5

The common ratio would be 10.

This is solving for r in its recurrence form

notes

Question 6

Finding the formula for the nth term

What does this practically mean?

Answer 6

Going from recurrence form to explicit in arithmetic standards

Question 7

What formula formula correctly represents the terms as successive powers of 1/2

Answer 7

Question 8

What is the common way to represent an alternating sign with an explicit fromula for a sequence?

Answer 8

(-1)^n

Question 9

Answer 9

Remember to think of a1 as a0. meaning its used to make the beginning (a=2)

Question 10

Solving problems with arithmetic series

What gives you the idea of the .. first term

Answer 10

It says “ a woman is able to walk a half-mile “
so a1= 1/2

Notes

Question 11

Solving problems with arithmetic series

What gives you the idea of the .. common difference (d)

Answer 11

It says “ Each Sunday, she walks an additional quarter-mile. “

So d= 1/4

Notes

Question 12

Solving problems with arithmetic series

The question asks for the total number of miles walked after 8 weeks, but this means what exactly?

How would you find a^8 ?

Answer 12

This means that n=8

Use the explicit formula for an arithmetic sequence. Notes

Question 13

Solving problems with arithmetic series

Solve the application problem.

Answer 13

Remember it says “adds” so it’s arithmetic not geometric.

Notes

Question 14

Solving problems with geometric series

What gives you the idea of the .. first term (a1)

Answer 14

It says that “the starting salary is $26,750”

so a1 is 27,750

Notes

Question 15

Solving problems with finite geometric series

What gives you the idea that this uses the partial sum formula.

Answer 15

It says: find the total amount earned at the end of 5 years

Notes

Question 16

Solving problems with finite geometric series

The question asks for the employee’s total earnings at the end of 5 years, but this means what exactly?

Answer 16

This means tha n=5

Notes

Question 17

Solving problems with geometric series

What gives you the idea of the .. common ratio (r)

Answer 17

It says 1.6%

Notes

Question 18

Solving problems with geometric series

Solve the application problem.

Answer 18

Notes

Question 19

Is a series defined?

1. How do you determine if a series sum is defined?
2. Given the first several terms of an infinite series, determine if the sum of the series exists.

Answer 19

examples

Question 20

given the infinite geometric series

Before finding the sum of an infinite series. You must determine if $?

Notes : Finding the sum of an infinite series

Answer 20

Confirm that the ratio is -1 < r < 1

Examples

Question 21

Telescope series

How do you know that Sk will converge or not?

What happens next

Answer 21

• Sk will converge if and only if {bk+1} converges to come finite number.
• And you find the limit of bn+1 to determine that finite number.

The sequence of the partial song converges to {b1-B} Notes

Question 22

Telescope series

What would S3 be?

Answer 22

{b1-b4}

Notes

Question 23

How do we know if the geometric series converges?

Its sequence of partial sums is given by {Sk}

Answer 23

Question 24

Answer 24

Question 25

What is the sum of the infinite series?

Answer 25

Question 26

To input the sum of the sequence using the sum() function on a TI-Nspire CX CAS, follow these steps:

Answer 26