Question 1

Find the sum.
-
A)-1,485
B)-1,435.5
C)-1,402.5
D)-1,287

Accepted Answer

The answer of Find the sum.
-
A)-1,485
B)-1,435.5
C)-1,402.5
D)-1,287...

Question 2

A geometric sequence is given. Find the common ratio and write out the first four terms.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of A geometric sequence is given. Find the...

Question 3

Solve.
-Suppose you just received a job offer with a starting salary of $37,000 per year and a guaranteed raise of$1500 per year. How many years will it be before youʹve made a total (or aggregate)salary of $1,025,000?
A)20 years
B)21 years
C)25 years
D)18 years

Accepted Answer

The total salary after n years is 37000 + 1500n. To find n, we solve 37000 + 1500n = 1025000. This gives n = 650. Since n represents the number of years, we round down to the nearest whole number, which is 20.

Question 4

Find the sum.
-
A)-1,798
B)-1,740
C)-1,711
D)-1,609.5

Accepted Answer

The answer of Find the sum.
-
A)-1,798
B)-1,740
C)-1,711
D)-1,609.5...

Question 5

Solve.
-A brick staircase has a total of 12 steps The bottom step requires 109 bricks. Each successive step requires 5less bricks than the prior one. How many bricks are required to build the staircase?
A)978 bricks
B)1,638 bricks
C)1,956 bricks
D)948 bricks

Accepted Answer

The total number of bricks required can be found using the formula for the sum of an arithmetic series. The first term (a) is 109 bricks, the common difference (d) is -5 (since each step requires 5 fewer bricks), and the number of terms (n) is 12. The sum (S) of an arithmetic series is given by S = n/2 [2a + (n-1)d]. Plugging in the values, we get S = 12/2 [2(109) + (12-1)(-5)] = 6 [218 - 55] = 6 * 163 = 978.

Question 6

Find the sum.
-
A)1,147
B)1,116
C)1,224.5
D)1,333

Accepted Answer

The answer of Find the sum.
-
A)1,147
B)1,116
C)1,224.5
D)1,333...

Question 7

Find the sum.
-7 + 14 + 21 + ... + 770
A)42735
B)42350
C) 
D)41965

Accepted Answer

The answer of Find the sum.
-7 + 14 + 21...

Question 8

Find the sum.
-
A)3,434
B)3,332
C)3,604
D)3,723

Accepted Answer

The answer of Find the sum.
-
A)3,434
B)3,332
C)3,604
D)3,723...

Question 9

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the
common difference; if it is geometric, find the common ratio.
-{4n - 3}
A)Arithmetic; d = 4
B)Geometric; r = 4
C)Arithmetic; d = -3
D)Neither

Accepted Answer

The given sequence is arithmetic because the term 4n - 3 increases by 4 as n increases by 1, making the common difference 4.

Question 10

A geometric sequence is given. Find the common ratio and write out the first four terms.
-
A) 
B) 
C)r 
D)

Accepted Answer

The answer of A geometric sequence is given. Find the...

Question 11

A geometric sequence is given. Find the common ratio and write out the first four terms.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of A geometric sequence is given. Find the...

Question 12

Find the sum.
-
A)304.1
B)47.96
C)256.14
D)212.08

Accepted Answer

The answer of Find the sum.
-
A)304.1
B)47.96
C)256.14
D)212.08...

Question 13

A geometric sequence is given. Find the common ratio and write out the first four terms.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of A geometric sequence is given. Find the...

Question 14

Solve.
-A theater has 36 rows with 25 seats in the first row, 30 in the second row, 35 in the third row, and so forth.How many seats are in the theater?
A)4,050 seats
B)4,140 seats
C)8,100 seats
D)8,280 seats

Accepted Answer

To find the total number of seats, we need to add up the number of seats in each row. We can use the formula for arithmetic series to do this: Sn = (n/2)(a1 + an), where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term. Using this formula, we find that the sum of the first 36 terms (number of rows) is 18(25 + 350) = 6,300. Therefore, the total number of seats is 6,300.

Question 15

A geometric sequence is given. Find the common ratio and write out the first four terms.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of A geometric sequence is given. Find the...

Question 16

Find the sum.
--3 + 1 + 5 + 9 + 13 + ... + (4n - 7)
A)n(2n - 5)
B)n(4n - 7)
C)n(2n + 5)
D)n(4n + 7)

Accepted Answer

This sequence is an arithmetic sequence with the first term $a_1 = -3$ and a common difference $d = 4$. The nth term of an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$. Substituting the given values, we get $a_n = -3 + (n - 1)4 = 4n - 7$, which matches the last term given in the question. The sum of the first n terms of an arithmetic sequence is given by $S_n = \frac{n}{2}(a_1 + a_n)$. Substituting the values, we get $S_n = \frac{n}{2}(-3 + 4n - 7) = \frac{n}{2}(4n - 10) = n(2n - 5)$, which corresponds to choice A.

Question 17

Find the sum.
-1 + 3 + 5 + ... + 539
A)72,900
B)73,170
C)73,441
D)72,361

Accepted Answer

The sum of the first n odd numbers is n^2. In this case, n = 269, so the sum is 269^2 = 72,900.

Question 18

Solve.
-A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3additional seats. How many seats are in the civic theater?
A)1092 seats
B)790 seats
C)1070 seats
D)1010 seats

Accepted Answer

The number of seats forms an arithmetic sequence with the first term $a_1 = 22$, common difference $d = 3$, and number of terms $n = 21$. The sum of an arithmetic series is given by $S_n = \frac{n}{2}[2a_1 + (n-1)d]$. Substituting the given values, $S_{21} = \frac{21}{2}[2(22) + (21-1)3] = \frac{21}{2}[44 + 60] = \frac{21}{2} \times 104 = 21 \times 52 = 1092$ seats.

Question 19

Find the sum.
-2 + 4 + 6 + ... + 1,298
A)421,850
B)421,201
C)420,552
D)422,500

Accepted Answer

We can use the formula for the sum of an arithmetic series: 
S = (n/2)(a + l) 
where S is the sum, n is the number of terms, a is the first term, and l is the last term.

In this case, a = 2, l = 1, and we need to find n. The common difference is 2, so to get from 2 to 1, we need to subtract 1 from the last even number, which is 1,298.

1,298 - 2 = 1,296 
1,296/2 = 648

So there are 648 terms in the sequence. Now we can plug in the values:

S = (648/2)(2 + 1) 
S = 324(3) 
S = 972

Therefore, the sum of the sequence is 972. However, none of the answer choices match this. We made an error in our sequence: the sequence should look like this:

2 + 4 + 6 + ... + 1,296 + 1,298

So we need to add the last two terms:

1,296 + 1,298 = 2,594

Now we can use the formula again:

1. There are 649 terms in the sequence.
2. The sum is (649/2)(2 + 1,298) = 421,850.

Therefore, the answer is A) 421,850.

Question 20

A geometric sequence is given. Find the common ratio and write out the first four terms.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of A geometric sequence is given. Find the...

Quiz 9: Sequences; Induction; the Binomial Theorem

Find the sum. -

A geometric sequence is given. Find the common ratio and write out the first four terms. -

Solve. -Suppose you just received a job offer with a starting salary of $37,000 per year and a guaranteed raise of$1500 per year. How many years will it be before youʹve made a total (or aggregate) salary of $1,025,000?

Find the sum. -

Solve. -A brick staircase has a total of 12 steps The bottom step requires 109 bricks. Each successive step requires 5less bricks than the prior one. How many bricks are required to build the staircase?

Find the sum. -

Find the sum. -7 + 14 + 21 + ... + 770

Find the sum. -

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. -{4n - 3}

A geometric sequence is given. Find the common ratio and write out the first four terms. -

A geometric sequence is given. Find the common ratio and write out the first four terms. -

Find the sum. -

A geometric sequence is given. Find the common ratio and write out the first four terms. -

Solve. -A theater has 36 rows with 25 seats in the first row, 30 in the second row, 35 in the third row, and so forth.How many seats are in the theater?

A geometric sequence is given. Find the common ratio and write out the first four terms. -

Find the sum. --3 + 1 + 5 + 9 + 13 + ... + (4n - 7)

Find the sum. -1 + 3 + 5 + ... + 539

Solve. -A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3additional seats. How many seats are in the civic theater?

Find the sum. -2 + 4 + 6 + ... + 1,298

A geometric sequence is given. Find the common ratio and write out the first four terms. -