Question 1

Write out the sum.
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A)1 + 3 + 5 + ... + (2n - 1)
B)3 + 5 + 7 + ... + (2n - 1)
C)1 + 3 + 5 + ... + (2n + 1)
D)3 + 5 +7+ ... + (2n + 1)

Accepted Answer

The answer of Write out the sum.
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A)1 + 3 +...

Question 2

Express the sum using summation notation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Express the sum using summation notation.
-
A) 
B)...

Question 3

Express the sum using summation notation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Express the sum using summation notation.
-
A) 
B)...

Question 4

Write out the sum.
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A)20 + 21 + 22 + ... + (n + 19)
B)n + 19
C)19 + 20 + 21 + ... + (n + 19)
D)1 + 2 + 3 + ... + n

Accepted Answer

The answer of Write out the sum.
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A)20 + 21 +...

Question 5

Express the sum using summation notation.
-3 + 6 + 9 + ... + 21
A) 
B) 
C) 
D)

Accepted Answer

The answer of Express the sum using summation notation.
-3 +...

Question 6

Write the word or phrase that best completes each statement or answers the question.
-Maria deposited $1500 in an independent retirement account at her bank. She earns 0.5% interest permonth on the balance. Each month, she deposits $100 in the account. Her balance each month after makinga $100 deposit, is given by the recursively defined sequence  If she made the initial deposit on September 30, and makes each monthly deposit on the last day of the monhow much money will be in the account at the end of the year for Maria to count as a deduction for that yeafederal income taxes? That is, determine

Accepted Answer

The answer of Write the word or phrase that best...

Question 7

Express the sum using summation notation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Express the sum using summation notation.
-
A) 
B)...

Question 8

Write out the sum.
-
A) 
B) 
C) 
D)

Accepted Answer

There is only a one-digit difference between the options in the fourth group of characters. The correct digit is 6, which is only present in option A. There is only a single character difference between the options, and the correct one can be deduced by looking at the previous section before the underscore. The previous section before the underscore in the given sum is 1f0b68784d69, which ends in 9. Option A has a previous section before the underscore that ends in 8, making it the closest match.

Question 9

Write out the sum.
-
A) 
B) 
C)3 + 12 + 27 + ... + 
D)1 + 2 + 3 + ... + n

Accepted Answer

The only difference between the given sum and the answer choice A is in the fourth set of digits (5456 instead of 5455). Therefore, this must be the correct answer choice. Option B has a different fourth set of digits compared to both the given sum and answer choice A. Option C is a sequence of numbers and not a hexadecimal value like the given sum, making it an invalid choice. Option D is a generic sequence sum and not related to the given sum. There is no indication of a mathematical sum in the given string of characters. The only difference between the options given is in the fifth set of characters, and option A is the only one that differs by one digit compared to the given string. Therefore, A is the best choice.

Question 10

Write out the sum.
-
A) 
B) 
C) 
D)0 + 1 + 2 + 3 + ... + n

Accepted Answer

The given sum is not a known sequence or formula, so we cannot use option D. The only difference between the options is the fourth digit of the second block (2d3c), so we need to compare them. The given sum ends with "edc19cfbc42b" and option A changes the fourth digit to 2d3d, which is only one-digit different. Therefore, option A is the most likely correct one.

Question 11

Express the sum using summation notation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Express the sum using summation notation.
-
A) 
B)...

Question 12

Express the sum using summation notation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Express the sum using summation notation.
-
A) 
B)...

Question 13

Write out the sum.
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A)12 + 15 + 18 + ... + (3n + 9)
B)3n + 9
C)9 +12 + 15 + ... + (3n + 9)
D)1 + 2 + 3 + ... + n

Accepted Answer

The answer of Write out the sum.
-
A)12 + 15 +...

Question 14

Express the sum using summation notation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Express the sum using summation notation.
-
A) 
B)...

Question 15

Write out the sum.
-
A) 
B) 
C)0 
D)

Accepted Answer

The answer of Write out the sum.
-
A) 
B) 
C)0 
D)...

Question 16

Write the word or phrase that best completes each statement or answers the question.
-Lexington Reservoir has 300 million gallons of water. About 0.07% of the water is lost to evaporation everyweek. About 150,000 gallons of water enter the reservoir every week. The amount of water in the reservoirat the end of each week is given by the recursively defined sequence  Determine the amount of water in the reservoir at the beginning of the second week. That is, determine

Accepted Answer

The answer of Write the word or phrase that best...

Question 17

Express the sum using summation notation.
-3 + 12 + 27 + . . . + 108
A) 
B) 
C) 
D)

Accepted Answer

The sequence is increasing by 3 each time, starting with 3. Therefore, we can represent it using the sum of an arithmetic series as: 
$$\sum_{i=1}^{10}(3i)$$
This notation represents the sum of each term in the sequence from the first term (3) to the 10th term (which is 3*10 = 30), where $i$ is the index of the current term. Simplifying the expression, we get: 
$$3\sum_{i=1}^{10}i$$
Which is equivalent to: 
$$3\cdot\frac{(10)(11)}{2}$$
Simplifying further, we get the sum as  165.

Question 18

Express the sum using summation notation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Express the sum using summation notation.
-
A) 
B)...

Question 19

Express the sum using summation notation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Express the sum using summation notation.
-
A) 
B)...

Question 20

Find the sum of the sequence.
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A)84
B)7
C)12
D)5

Accepted Answer

The answer of Find the sum of the sequence.
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A)84
B)7
C)12
D)5...

Quiz 9: Sequences; Induction; the Binomial Theorem

Write out the sum. -

Express the sum using summation notation. -

Express the sum using summation notation. -

Write out the sum. -

Express the sum using summation notation. -3 + 6 + 9 + ... + 21

Express the sum using summation notation. -

Write out the sum. -

Write out the sum. -

Write out the sum. -

Express the sum using summation notation. -

Express the sum using summation notation. -

Write out the sum. -

Express the sum using summation notation. -

Write out the sum. -

Express the sum using summation notation. -3 + 12 + 27 + . . . + 108

Express the sum using summation notation. -

Express the sum using summation notation. -

Find the sum of the sequence. -