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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 a₁ and the common difference d.

a.Find a₇ when a₁ = –8 and d = 4.

b.Find a₁₆ when a₁ = 10 and d = 7.

2)Write a formula for the n^th term of each arithmetic sequence. Then use the formula to find a₁₅.

a.3, 8, 13, 18

b.a₁ = –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.a₁ = 5 and r = 2

b.a₁ = 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.(2x – 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?

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