# number theory 1

**Assignment 12.1: Applying Number Theory **

Complete the following problems. Be sure to show all work.

1)Find the indicated term of the arithmetic sequence with the first term *a*_{1} and the common difference *d*.

a.Find *a*_{7} when *a*_{1 }= â€“8 and *d* = 4.

b.Find *a*_{16} when *a*_{1 }= 10 and *d* = 7.

2)Write a formula for the *n*^{th} term of each arithmetic sequence. Then use the formula to find *a*_{15}.

a.3, 8, 13, 18

b.*a*_{1 }= â€“3 and *d* = 6

3)Find the sum of the even integers between 30 and 70.

4)Find the indicated sum.

a.

b.

5) Write the first four terms of each geometric sequence.

a.*a*_{1 }= 5 and *r* = 2

b.*a*_{1 }= 6 and

6)Find the indicated sum.

a.

b.

7)Find the sum of the infinite geometric series.

8)Use mathematical induction to prove that the following statement is true for every positive integer *n*.

9)Use the Binomial Theorem to expand each binomial and express the result in simplified form.

a.(*x* + 7)^{4 }

b.(2*x* â€“ 1)^{5} ^{}

10)A jury pool of consists of 50 potential jurors. In how many ways can a jury of 12 be selected?

11)A 10 member club is getting ready to select a president and secretary. Assuming that the same person cannot hold each job, how many ways can the offices be filled?

12)Jenny has 10 tops, 6 bottoms, 3 belts, and 5 pairs of shoes. Assuming that everything matches, how many different outfits can Jenny create?