Question 1

Write a formula for the nth term of the given arithmetic sequence. 4, 10, 16, 22, 28, . . . A) a_n = 6n - 2 B) a_n = 7n - 3 C) a_n = 6n + 2 D) a_n = 2n - 6

Accepted Answer

The common difference in the sequence is 6 (each term increases by 6). The first term is 4. The formula for the nth term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term and $d$ is the common difference. Substituting $a_1 = 4$ and $d = 6$ gives $a_n = 4 + (n - 1)6 = 6n - 2$.

Question 2

Complete the rewriting of the given series using the new index as indicated.  &#10;A)&#10; &#10;B)&#10; &#10;C)&#10; &#10;D)&#10;

Accepted Answer

11ea9079_e2d6_7805_aec7_bd14ba5140d3_TB3543_11

Question 3

Evaluate   .&#10;A) 1&#10;B) Undefined&#10;C) 6&#10;D) 0

Accepted Answer

1

Question 4

Suppose a deposit of $500 is made at the beginning of each year for 15 years into an account that pays 9% compounded annually. What is the amount of this annuity at the end of the 15^th year? A) $16,501.70 B) $18,486.85 C) $13,009.59 D) $16,001.70

Accepted Answer

The answer of Suppose a deposit of $500 is made...

Question 5

Find the sum of the given geometric series.  &#10;A) -19,682&#10;B) -59,048&#10;C) -177,146&#10;D) -6,560

Accepted Answer

The answer of Find the sum of the given geometric...

Question 6

Find the sum of the given infinite geometric series.  &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Find the sum of the given infinite...

Question 7

Write the first five terms of the arithmetic sequence whose nth term is given. a_n = -3 + (n - 2)(-3) A) -6, -3, 0, 3, 6 B) 3, 0, -3, -6.0, -9 C) 3, 0, -3, -6, -9 D) 0, -3, -6, -9, -12

Accepted Answer

The answer of Write the first five terms of the...

Question 8

Use the binomial theorem to expand the given binomial. (t + 2)⁴ A) t⁴ + 8t³ + 12t² + 8t + 2 B) t⁴ + 8t³ + 24t² + 32t + 16 C) 2t⁴ + 16t³ + 48t² + 16t + 2 D) t⁴ + 2t³ + 4t² + 8t + 16

Accepted Answer

Using the binomial theorem, we have:
(t + 2)^7 = 
C(7,0)t^7(2)^0 + C(7,1)t^6(2)^1 + C(7,2)t^5(2)^2 + C(7,3)t^4(2)^3 + C(7,4)t^3(2)^4 + C(7,5)t^2(2)^5 + C(7,6)t^1(2)^6 + C(7,7)t^0(2)^7
Simplifying this gives:
tS1U1P14S1S1P0 + 8tS1U1P13S1S1P0 + 28tS1U1P12S1S1P0 + 56tS1U1P11S1S1P0 + 70tS1U1P10S1S1P0 + 56tS1U1P9S1S1P0 + 28tS1U1P8S1S1P0 + 8tS1U1P7S1S1P0 + 2tS1U1P6S1S1P0

Therefore, the best choice is B.

Question 9

Find the common difference of an arithmetic sequence if the first term is -9 and the seventh term is -39.&#10;A) -4&#10;B) 3&#10;C) -6&#10;D) -5

Accepted Answer

The common difference (d) in an arithmetic sequence can be found using the formula for the nth term: $a_n = a_1 + (n - 1)d$, where $a_n$ is the nth term, $a_1$ is the first term, and $n$ is the term number. Substituting the given values for the 7th term, we get $-39 = -9 + (7 - 1)d$, which simplifies to $-30 = 6d$. Solving for $d$ gives $d = -5$.

Question 10

Write the first four terms of the geometric sequence whose nth term is given. a_n = (-6)ⁿ^-1 A) 1, -6, 36, -216 B) 0, -6, 36, -216 C) 1, 6, 36, 216 D) -6, 36, -216, 1296

Accepted Answer

The nth term of the sequence is given by a_n = (-6)^n-1. Substituting n = 1, 2, 3, and 4, we get the terms: 1, -6, 36, -216.

Question 11

Find   .&#10;A) -13&#10;B) 13&#10;C) 0&#10;D) -1

Accepted Answer

The answer of Find   .&#10;A) -13&#10;B) 13&#10;C) 0&#10;D)...

Question 12

Find   .&#10;A) 24&#10;B) 70&#10;C) 14&#10;D) 18

Accepted Answer

The answer of Find   .&#10;A) 24&#10;B) 70&#10;C) 14&#10;D)...

Question 13

List the first four terms of the given sequence and match your result to the correct answer below. c_n = (-1)ⁿ(-2n + 3)² A) 1, -1, 9, -25 B) 1, -1, 1, -9 C) 1, -9, 25, -49 D) -1, 1, -9, 25

Accepted Answer

The answer of List the first four terms of the...

Question 14

List all terms of the given finite sequence and match your result to the correct answer below. c_n = (-1)^n-³ for 3 $\le$ n $\le$ 7 A) -1, 1, -1, 1, -1 B) 1, 1, 1, 1, 1 C) 1, -1, -1, -1, -1 D) 1, -1, 1, -1, 1

Accepted Answer

The answer of List all terms of the given finite...

Question 15

Write the given series in summation notation. Use the index i, and let i begin at 1. ln(9) + ln(10) + ln(11)&#10;A)   ln(i + 9)&#10;B)   ln(i + 8)&#10;C)   ln(i)&#10;D)   ln(i + 7)

Accepted Answer

The answer of Write the given series in summation notation....

Question 16

Find the sum of the given series.  &#10;A) 9&#10;B) -27&#10;C) -108&#10;D) -36

Accepted Answer

The answer of Find the sum of the given series....

Question 17

Write a formula for the nth term of the given geometric sequence. 3, -6, 12, ... A) a_n = -3(2)ⁿ^-1 B) a_n = 3(-2)ⁿ⁺¹ C) a_n = 3(-2)ⁿ^-1 D) a_n = 3(-2)ⁿ

Accepted Answer

The answer of Write a formula for the nth term...

Question 18

List all terms of the finite sequence a_n = 6n + 2 for 1 ≤ n ≤ 5. A) 8, 14, 20, 26, 32 B) 8, 10, 12, 14, 16 C) 9, 10, 11, 12, 13 D) 1, 2, 3, 4, 5

Accepted Answer

The answer of List all terms of the finite sequence...

Question 19

Each time an aluminum beverage can is recycled, some amount of the material is lost due to a variety of reasons. If each recycling step is 90% efficient, what percent of the original material remains if a can is recycled 6 times? Round to the nearest tenth of a percent.

A) 63.2%
B) 56.5%
C) 57.9%
D) 53.1%

Accepted Answer

The answer of Each time an aluminum beverage can is...

Question 20

Write a formula for the general term of the given sequence and match your result to the correct answer below. -2, -1, 0, 1, 2, ... A) a_n = (-1)ⁿ(n - 3) B) a_n = n - 3 C) a_n = -n - 3 D) a_n = n + 3

Accepted Answer

The answer of Write a formula for the general term...

Question 21

Use the binomial theorem to write out the first four terms of the given binomial. (x² + 1)¹⁷ A) x¹⁷ + 17x¹⁶ + 136x¹⁵ + 680x¹⁴ B) x³⁴ + 17x³² + 136x³⁰ + 680x²⁸ C) x¹⁷ + 17x³³ + 136x³² + 680x³¹ D) x³⁴ + 17x³³ + 136x³² + 680x³¹

Accepted Answer

The answer of Use the binomial theorem to write out...

Deck 14: Section 1: Sequences and Series Available Online at Www.mhhe.com/dugopolski