List the first five terms of the sequence with initial terms u 1 = 1 and u 2 = 5, and, for n ≥ 3, u n = 5u n−1 − 6u n−2

(1) What is the 50 th term of the arithmetic sequence with initial term 4 and common

difference 3?

7

(2) Evaluate

4

X

k=−3

(2k + 5). (Hint: Since there are only eight terms in the sum, you can just

write them all out and add.)

(3) Evaluate

99

X

i=0

?

− 2

3

? i

. (Hint: Since there are 100 terms in the sum, it isn’t a good idea to

write them all out and add. Use the formula for the sum of terms of a geometric sequence.

Leave the answer with exponents rather than using a calculator to try to get a decimal

(4) (a) List the first four terms of the sequence defined recursively by a 0 = 2, and, for n ≥ 1,

a n = 2a 2

n−1 − 1.

(b) List the first five terms of the sequence with initial terms u 1 = 1 and u 2 = 5, and, for

n ≥ 3, u n = 5u n−1 − 6u n−2 . Guess a closed form formula for the sequence. Hint: The

terms are simple combinations of powers of 2 and powers of 3.

(5) Give a recursive definition of the geometric sequence with initial term a and common

ratio r.

Hint: a n = ar n−1 isn’t a correct answer since this formula isn’t recursive. Make sure you

write down a recursive formula: (1) give the initial term, and (2) give the rule for building

new terms from previous terms.

(6) (bonus) Express in summation notation:

1

2

+

1

4

+

1

6

• ··· +

1

2n , the sum of the reciprocals

of the first n even positive integers. (Note that there are n terms in the sum.)

Hint: A common mistake on this question is using the symbol n both as an index for

summation and to indicate the last term to be added in. To make sure you haven’t fallen

into that trap, replace every n in your formula by a specific value, say 5. The result shouldbe a sum

1

2

+

1

4

+

1

6

+

1

8

+

1

10

Kidney dialysis

Give a concise explanation of what is kidney dialysis in a well thought paper. include 2-3 references in your work. No plagiarism Related

Discuss the importance of Interdisciplinary team collaboration and communication in HC related managerial situation

Question description Discuss the importance of Interdisciplinary team collaboration and communication in HC related managerial situations. Offer minimum 1 advantage of the established communication and one disadvantage of the failed….

Provide an explanation of the financial concept(s)

Question description From the list of financial concepts, pick 1-2 financial concepts. Search for a healthcare finance related article on the concepts. In a 3-5 page paper, describe how you can apply….