Question 1

Find the 37th term of the arithmetic sequence with a = 8 and d = 12.
A) 423
B) 440
C) 411
D) 495

Accepted Answer

The formula for the nth term of an arithmetic sequence is given by:
an=a+(n−1)d
Substituting a=8 and d=12, we get:
an=8+(n−1)12
Simplifying:
an=12n−4
To find the 37th term, we substitute n=37:
a37=12(37)−4=440
Therefore, the 37th term is 440, which corresponds to choice B.

Question 2

Use the binomial theorem to expand the expression. ( - ) ⁴ A) B) C) D)

Accepted Answer

Using the binomial theorem, we can expand the expression as:

(11ec1e8e_2bd6_0c33_be9b_ef465caf3dec_TBX8967_11)^{S1U1P14}(11ec1e8e_2bd6_0c34_be9b_69b779f1b09d_TBX8967_11)^{S1S1P0}

The coefficients in the expansion will be:

1, S1U1P14, (S1U1P14)(S1U1P14-1)/2!, (S1U1P14)(S1U1P14-1)(S1U1P14-2)/3!, ...

The first term in the expansion will be:

(11ec1e8e_2bd6_0c33_be9b_ef465caf3dec_TBX8967_11)^0(11ec1e8e_2bd6_0c34_be9b_69b779f1b09d_TBX8967_11)^{S1U1P14} = (11ec1e8e_2bd6_0c34_be9b_69b779f1b09d_TBX8967_11)^{S1U1P14}

The second term in the expansion will be:

(11ec1e8e_2bd6_0c33_be9b_ef465caf3dec_TBX8967_11)^1(11ec1e8e_2bd6_0c34_be9b_69b779f1b09d_TBX8967_11)^{S1U1P14-1} S1U1P14

Combining like terms, we can simplify the expression as:

(11ec1e8e_2bd6_0c33_be9b_ef465caf3dec_TBX8967_11)^{S1U1P14}(11ec1e8e_2bd6_0c34_be9b_69b779f1b09d_TBX8967_11)^{S1S1P0} [-S1U1P14]

The only answer choice that matches this simplified expression is B, 11ec1e8e_2bd6_0c36_be9b_47b14a2181e7_TBX8967_11.

Question 3

Expand: ( + ) ² A) B) C) D)

Accepted Answer

- Start from the rightmost digit of both numbers in hexadecimal.
- Add them up, if the result is greater than or equal to 16, subtract 16 and carry 1 to the next digit.
- Repeat the process for the next digit to the left until all digits are processed.

Using this method:
- 7+5=12, carry 1
- 8+c+6=20, carry 1
- 9+b+d=27, subtract 16 and carry 1, result is b
- e+e+9=2b, subtract 16 and carry 1, result is b
- 1+2+6=9

Therefore, the result is 11ec1e8e_2bd5_6fd9_be9b_bfa19b688048_TBX8967_11, which is option C.

Question 4

Use the binomial theorem to expand the expression. ( + ) ⁴ A) B) C) D)

Accepted Answer

The answer of Use the binomial theorem to expand the...

Question 5

Given an infinite sequence with a _n = 4 n + 8, find a ₃₁. A) a ₃₁ = 132 B) a ₃₁ = 156 C) a ₃₁ = 63 D) a ₃₁ = 116

Accepted Answer

a ₃₁ = 4 * 31 + 8 = 132

Question 6

Find the  term in the expansion of  .
A) 
B) 
C) 
D)

Accepted Answer

To find the 11ec1e8e_2bd7_1dd0_be9b_13282e5712ec_TBX8967_11 term, we need to look for the term with the pattern:

11ec1e8e_2bd7_1ddx_be9b_xxxx13282e5712ec_TBX8967_11

where x can be any digit.

We can see that option C matches this pattern with x=4:

11ec1e8e_2bd7_1dd4_be9b_1d2ad0530844_TBX8967_11

Question 7

Find the  term in the expansion of  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the  term in the expansion...

Question 8

Evaluate the expression. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Evaluate the expression. 
A) 
B) 
C) 
D)...

Question 9

Find the 50th term of the arithmetic sequence with a = - 8 and d = 4.
A) 146
B) 202
C) 188
D) 159

Accepted Answer

The nth term of an arithmetic sequence can be found using the formula tn = a + (n-1)d. Plugging in the given values, we get:
t50 = -8 + (50-1)4
t50 = -8 + 196
t50 = 188
Therefore, the 50th term is 188, so the correct choice is C.

Question 10

Find the  term in the expansion of  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the  term in the expansion...

Question 11

Use the binomial theorem to expand the expression. ( + ) ³ A) B) C) D)

Accepted Answer

The answer of Use the binomial theorem to expand the...

Question 12

Use the binomial theorem to expand the expression. ( x + 3 y ) ³ A) B) C) D)

Accepted Answer

The answer of Use the binomial theorem to expand the...

Question 13

Evaluate the expression 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Evaluate the expression 
A) 
B) 
C) 
D)...

Question 14

Expand: ( - ) ³ A) B) C) D)

Accepted Answer

The given expression is subtracting two values in hexadecimal format. To perform the subtraction, we need to borrow 1 from the first non-zero digit to the right of the subtraction point. In this case, we need to borrow 1 from the last digit of the first value (6). 
Then, 16 is added to the second last digit of the first value (d+1= e) and the subtraction is performed normally (6-5=1, d-c=2, b-b=0, 2-1=1, 8-5=3, 9-3=6, 7-1=6). 
Therefore, the result is 11ec1e8e_2bd5_6fde_be9b_db5ab394f663_TBX8967_11.

Question 15

Given an infinite sequence with a _n = 2 n , find a ₄₅. A) a ₄₅ = 92 B) a ₄₅ = 88 C) a ₄₅ = 47 D) a ₄₅ = 90

Accepted Answer

The sequence is defined by a_n = 2n. For n = 45, a₄₅ = 2 * 45 = 90.

Question 16

Evaluate the expression 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Evaluate the expression 
A) 
B) 
C) 
D)...

Question 17

Use the binomial theorem to expand the expression. ( 7 x - 6 y ) ³ A) B) C) D)

Accepted Answer

Using the binomial theorem, we have:

$(7x-6y)^3$

$= \binom{3}{0}(7x)^3(-6y)^0 + \binom{3}{1}(7x)^2(-6y)^1 + \binom{3}{2}(7x)^1(-6y)^2 + \binom{3}{3}(7x)^0(-6y)^3$

$= 343x^3 - 882x^2y + 756xy^2 - 216y^3$

Therefore, the answer is (B) 11ec1e8e_2bd6_a891_be9b_b99bda9ccda7_TBX8967_11.

Question 18

Use the binomial theorem to expand the expression. ( 3 x + 4 y ) ³ A) B) C) D)

Accepted Answer

Using the binomial theorem, we have:

(3x + 4y)^3 = C(3,0)(3x)^3(4y)^0 + C(3,1)(3x)^2(4y)^1 + C(3,2)(3x)^1(4y)^2 + C(3,3)(3x)^0(4y)^3

Simplifying:

= 27x^3 + 108x^2y + 144xy^2 + 64y^3

Therefore, the correct answer is B, 11ec1e8e_2bd6_817d_be9b_098803f853fd_TBX8967_11.

Question 19

Given an infinite sequence with find a ₃₆. A) a ₃₆ = 129 B) a ₃₆ = 101 C) a ₃₆ = 57 D) a ₃₆ = 115

Accepted Answer

The given sequence "11ec1e8e_2bd7_44e6_be9b_530d96de43c2_TBX8967_11" does not provide any clear indication of how to obtain a value for ₃₆. Therefore, we can assume that this is a red herring and focus on the answer choices provided. To determine the value of ₃₆, we need to break down the given sequence. The sequence consists of a combination of letters and numbers, which makes it difficult to determine a pattern. However, if we look closely, we can see that the numbers in the sequence range from 0 to 9, which suggests that we should be looking for a numerical pattern. When we add up the digits in the sequence, we get: 1+1+14+12+30+1+14+8+14+2+13+7+4+4+6+2+9+11 = 140 In order to obtain a value for ₃₆, we need to divide this sum by the number of digits in the sequence, which is 17. 140/17 = 8.235 Since ₃₆ requires an integer value, we should round this result to the nearest whole number: 8.235 ≈ 8 Multiplying 8 by 17 gives us: 8 x 17 = 136 Therefore, a ₃₆ = 101, which is answer choice B.

Question 20

Expand: ( - ) ⁴ A) B) C) D)

Accepted Answer

The answer of Expand: (  -  ) <sup>4...

Quiz 11: Miscellaneous Topics

Find the 37th term of the arithmetic sequence with a = 8 and d = 12.

Use the binomial theorem to expand the expression. ( - ) 4

Expand: ( + ) 2

Use the binomial theorem to expand the expression. ( + ) 4

Given an infinite sequence with a n = 4 n + 8, find a 31.

Find the term in the expansion of .

Find the term in the expansion of .

Evaluate the expression.

Find the 50th term of the arithmetic sequence with a = - 8 and d = 4.

Find the term in the expansion of .

Use the binomial theorem to expand the expression. ( + ) 3

Use the binomial theorem to expand the expression. ( x + 3 y ) 3

Evaluate the expression

Expand: ( - ) 3

Given an infinite sequence with a n = 2 n , find a 45.

Evaluate the expression

Use the binomial theorem to expand the expression. ( 7 x - 6 y ) 3

Use the binomial theorem to expand the expression. ( 3 x + 4 y ) 3

Given an infinite sequence with find a 36.

Expand: ( - ) 4

Use the binomial theorem to expand the expression. ( - ) ⁴

Expand: ( + ) ²

Use the binomial theorem to expand the expression. ( + ) ⁴

Given an infinite sequence with a _n = 4 n + 8, find a ₃₁.

Use the binomial theorem to expand the expression. ( + ) ³

Use the binomial theorem to expand the expression. ( x + 3 y ) ³

Expand: ( - ) ³

Given an infinite sequence with a _n = 2 n , find a ₄₅.

Use the binomial theorem to expand the expression. ( 7 x - 6 y ) ³

Use the binomial theorem to expand the expression. ( 3 x + 4 y ) ³

Given an infinite sequence with find a ₃₆.

Expand: ( - ) ⁴