Test Name: Test 4 Practice Fall 2104
1.
Determine the first five terms of the sequence whose 𝑛𝑡ℎ term is defined as follows. Please simplify your solution.
𝑎𝑛 = −4𝑛 − 3
2.
Determine the first five terms of the sequence whose 𝑛𝑡ℎ term is defined as follows. Please simplify your solution.
1 𝑛−1
𝑎𝑛 = ( )
+ 7
4
3.
Translate the summation notation that follows into an expanded sum. Then use the formulas and properties of summation to
evaluate the sums. Please simplify your solution.
6
∑(2𝑖 + 2)
𝑖=2
4.
Find a possible formula for the general 𝑛𝑡ℎ term of the sequence that begins as follows. Please simplify your solution.
1 1 1 1
1, , , , , . . ..
4 9 16 25
5.
Find a possible formula for the general 𝑛𝑡ℎ term of the sequence that begins as follows. Please simplify your solution.
−4, −5, −6, −7, −8, . ..
6.
Find the explicit formula for the general 𝑛𝑡ℎ term of the arithmetic sequence described below. Simplify your answer.
−11, 1, 13, 25, 37, . ..
7.
Find the explicit formula for the general 𝑛𝑡ℎ term of the arithmetic sequence described below. Simplify your answer.
𝑎1 = −19 and 𝑎4 = −10
8.
Find the explicit formula for the general 𝑛𝑡ℎ term of the arithmetic sequence described below. Simplify your answer.
𝑎21 = 103 and 𝑑 = 5
9.
Given that 𝑎 is an arithmetic sequence, 𝑎1 = −10 and 𝑎6 = 5 , what is 𝑎54 ?
1
10.
The following sum is a partial sum of an arithmetic sequence; use either formula for finding partial sums of arithmetic
sequences to determine its value.
95
∑(−3𝑖 + 6)
𝑖=6
11.
Find the explicit formula for the general 𝑛𝑡ℎ term of the geometric sequence described below.
−10, 10, −10, 10, −10, . ..
Enter your answer as a fraction in simplest terms.
12.
Find the explicit formula for the general 𝑛𝑡ℎ term of the geometric sequence described below.
50421
𝑎5 =
and 𝑟 = 7
2
13.
Find the explicit formula for the general 𝑛𝑡ℎ term of the geometric sequence described below.
𝑎4 = 135 and 𝑎7 = 3645 and 𝑟 > 0
14.
Given that 𝑎 is a geometric sequence and 𝑎2 = 12 , and 𝑎5 = −96 , what is the common ratio 𝑟 ?
15.
Write the following repeating decimal number as a fraction.
7. ̅̅̅̅̅
281
16.
The following can be answered by finding the sum of a finite or infinite geometric sequence. Round the solution to 2
decimal places.
If $21,000 is invested in an IRA account with an annual interest rate of 4% compounded once a year, what is the value of the
account after 14 years?
17.
The following sum is a partial sum of a geometric sequence. Use this fact to evaluate the sum.
7
∑( −3 )𝑖
𝑖=2
2
18.
How many different 7-digit phone numbers do not contain the digit 6? Assume that any digit in the phone number can be
any of the remaining numbers. Use the Multiplication Principle of Counting to solve the problem.
19.
A license plate must contain 3 numerical digits followed by 3 letters. If the first digit cannot be 1, how many different
license plates can be created? Use the Multiplication Principle of Counting to solve the problem.
20.
At a meeting of 14 people, a president, vice president, secretary, and treasurer are to be chosen. How many different ways
can these positions be filled? Express the answer to the permutation problem using permutation notation ( 𝑛 𝑃𝑘 ) and
numerically.
Answer: Permutation Notation:
21.
P
Value:
A trade union asks its members to select 3 people, from a slate of 12, to serve as representatives at a national meeting. How
many different sets of 3 can be chosen? Express the answer to the combination problem using combination notation ( 𝑛 𝐶𝑘 )
and numerically.
Answer: Combination Notation:
C
Value:
22.
Expand the expression (2𝑥 + 𝑦)5. Use the Binomial and Multinomial Theorems to solve the problem. Write the answer
starting with decreasing powers of 𝑦 and increasing powers of .
23.
An ordinary die is rolled. Find the probability of rolling an even non-prime number. Write your answer as a fraction in
simplest form or round any decimals to 4 decimal places. Be careful to properly identify the sample space and the
appropriate event.
24.
A card is drawn from a standard 52-card deck. Find the probability of drawing a face card ( Jack, Queen, or King ) in the suit
of Diamonds. Write your answer as a fraction in simplest form or round any decimals to 4 decimal places. Be careful to
properly identify the sample space and the appropriate event.
25.
A coin is flipped 4 times. Find the probability of getting heads exactly 2 times. Write your answer as a fraction in simplest
form or round any decimals to 4 decimal places. Be careful to properly identify the sample space and the appropriate event.
3