MAC 1140Test 4 Review andPractice Solutions

MAC 1140 Test 4 Review 12.1 – 12.5 • You will need to have your own graphing calculator for the test. • You may not share calculators or use any type of communication device in place of a calculator. • Tests cannot be made up for any reason other than an NWFSC event for which you must miss class. • If you miss one test, your final exam score will be substituted. A second missed test is a zero.

Exam TopicsObjective Section Suggested Text Problems

1) Write out the first five terms of a sequence. 12.1 p. 838: 1, 32) Find the sum of a sequence. 12.1 p. 838: 13, 153) Find the indicated term of an arithmetic sequence. 12.2 p. 838: 174) Find a general formula for a given arithmetic sequence. 12.2 p. 838: 215) Work with applications of arithmetic sequences. 12.2 p. 839: 34(a)8,(b)11006) Find the indicated term of a geometric series. 12.3 p. 838: 197) Determine whether a geometric series converges or diverges (and determine the sum if it converges). 12.3 p. 838: 23, 258) Prove statements using mathematical induction. 12.4 p. 839: 279) Use the Binomial theorem to expand a binomial 12.5 p. 839: 31, 3310) Use the Binomial theorem to find a particular coefficient in a binomial expansion. 12.5 p. 836: 29, 31

To Study for the Test• Complete all assigned homework. Remember that a score of at least 70% on each assignment gives you 10 bonus points on the test.• Complete the practice test and check your solutions.• Set up a study system (note cards for example) for each of the 10 objectives in the chart above.• Review your notes and applicable problem set questions for each of the 10 objectives in the chart above.• Work the suggested text problems for each of the 12 objectives in the chart above.

Things to KnowSummation Formulas      

Arithmetic Sequences 

 Geometric Sequences

Geometric Series Converges if with sum  

Mathematical Induction1) Show that the statement is true for 2) Show that if the statement is true for , then it’s true for 3) Conclude that the statement is true for all natural numbers

Binomial TheoremStart with The exponents of subsequent terms go up with the constant and down with the variable.

1) Find the first five terms of a)

b)

2) Find each suma)

b)

3) Find the 120th term of

4) Find the first term, common difference, and a simplified formula for the nth term of the arithmetic sequence where the 7th term is 4 and the 22nd term is 34.

4) Find the first term, common difference, and a simplified formula for the nth term of the arithmetic sequence where the 7th term is 4 and the 22nd term is 34.OR

5) When Eric started work as an orange picker, he picked 10 oranges in the first minute, 12 in the second minute, 14 in the third minute, and so on. How many oranges did Eric pick in the first 30 minutes?

6) a) Find the sixth term of

b) Find the seventh term of

Find the nth term of

7) Determine whether each series converges or diverges. If it converges, find its sum.a)

b)

8) a) Answer the following questions to prove by mathematical induction that

1) Show that the statement is true for 2) What is the right hand side if (in factored form)?3) What is the right hand side if (in factored form)?4) Use the information in number 2 to show that the statement in number 3 is true.

b) Answer the following questions to prove by mathematical induction that 1) Show that the statement is true for 2) What is the right hand side if (in factored form)?3) What is the right hand side if (in factored form)?4) Use the information in number 2 to show that the statement in number 3 is true

9) Expand each binomial using the binomial theorem. You may use your calculator to compute the combinations.a) ++++1

b) +++1

 10) Use the binomial theorem to answer each question. You may use your calculator to compute the combinations.a) What is the coefficient of in The two exponents must add up to 12.

b) What is the third tem of The third term has an exponent on the constant term of one less than the term. Since the term is the third, it’s an exponent of 2.OR The exponent on the variable counts down → 8, 7, 6. The exponent on the variable is 6.In either case, the term is:

Test 4 Extra Practice

1) Find the sum:

1) Find the sum:

2) Find the 90th term of

2) Find the 90th term of

3)A brick driveway has 50 rows of bricks. The first row has 16 bricks and the fiftieth row has 65 bricks. Assuming that the number of bricks in each row forms an arithmetic sequence, what is total number of bricks?

3)A brick driveway has 50 rows of bricks. The first row has 16 bricks and the fiftieth row has 65 bricks. Assuming that the number of bricks in each row forms an arithmetic sequence, what is total number of bricks?

4) Determine whether the series converges or diverges. If it converges, find its sum.a)

4) Determine whether the series converges or diverges. If it converges, find its sum.a)

 5) Use the binomial theorem to answer the question. You may use your calculator to compute the combinations.What is the coefficient of in

 5) Use the binomial theorem to answer the question. You may use your calculator to compute the combinations.What is the coefficient of in The two exponents must add up to 12.