Question 1

Find the sum of the arithmetic sequence.
-2 + 4 + 6 + ... + 678
A) 115,260
B) 114,582
C) 115,600
D) 114,921

Accepted Answer

The sum of an arithmetic sequence can be found using the formula $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the sum of the first $n$ terms, $a_1$ is the first term, $a_n$ is the nth term, and $n$ is the number of terms. Here, $a_1 = 2$, $a_n = 678$, and the common difference $d = 2$. To find $n$, we use the formula for the nth term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$. Substituting the given values, we get $678 = 2 + (n - 1)2$, which simplifies to $676 = 2(n - 1)$, so $n = 339$. Substituting $n$, $a_1$, and $a_n$ into the sum formula gives $S_n = \frac{339}{2}(2 + 678) = 169.5 \times 680 = 115,260$.

Question 2

Find the sum of the arithmetic sequence.
-(-6) + (-1) + 4 + 9 + ... + 39
A) 330
B) 170
C) 160
D) 165

Accepted Answer

The given sequence is an arithmetic sequence with the first term $a_1 = -6$ and a common difference $d = 5$. The last term $a_n = 39$. To find the sum $S_n$ of the sequence, we first need to find the number of terms $n$. We can use the formula for the $n$th term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$. Substituting the given values, we get $39 = -6 + (n - 1)5$. Solving for $n$, we find $n = 10$. Now, we can use the formula for the sum of the first $n$ terms of an arithmetic sequence: $S_n = \frac{n}{2}(a_1 + a_n)$. Substituting the known values, we get $S_n = \frac{10}{2}(-6 + 39) = 5 \times 33 = 165$.

Question 3

Find the sum of the arithmetic sequence.
-6 + 12 + 18 + ... + 492
A) 20172
B) 19926
C) 20418
D) 20667

Accepted Answer

The answer of Find the sum of the arithmetic sequence.
-6...

Question 4

Find the sum of the arithmetic sequence.
-1 + 2 + 3 + ... + 707
A) 250278
B) 500,556
C) 499,849
D) 249571

Accepted Answer

The sum of an arithmetic sequence can be found using the formula $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the sum of the first $n$ terms, $a_1$ is the first term, $a_n$ is the nth term, and $n$ is the number of terms. Here, $a_1 = 1$, $a_n = 707$, and $n = 707$. Plugging these values into the formula gives $S_n = \frac{707}{2}(1 + 707) = 353.5 \times 708 = 250278$.

Question 5

Solve the problem.
-The population of a town is increasing by 300 inhabitants each year. If its population at the beginning of 1990 was 23,626, what was its population at the beginning of 1997?
A) 330,638 inhabitants
B) 165,319 inhabitants
C) 25,726 inhabitants
D) 25,426 inhabitants

Accepted Answer

The population increases by 300 inhabitants each year. From 1990 to 1997 is 7 years. So, the increase is 300 inhabitants/year * 7 years = 2100 inhabitants. The population at the beginning of 1997 is 23,626 + 2,100 = 25,726 inhabitants.

Question 6

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -6th term is -10; 15th term is -46 A) a1 = -10, d = -4, a_n = a_n- 1 - 4 B) a1 = 10, d = -4, a_n = a_n- 1 - 4 C) a1 = -30, d = 4, a_n = a_n- 1 + 4 D) a1 = 10, d = 4, a_n = a_n- 1 + 4

Accepted Answer

The common difference d is calculated as (-46 - (-10)) / (15 - 6) = -4. Using the 6th term, -10 = a1 + 5(-4), we find a1 = 10. The recursive formula is a_n = a_n-1 - 4.

Question 7

Find the sum of the arithmetic sequence.
-{3n + 7}, n = 48
A) 3864
B) 4032
C) 4200
D) 3792

Accepted Answer

The sum of the first n terms of an arithmetic sequence is given by the formula:S = n/2 * (2a + (n-1)d)where a is the first term, d is the common difference, and n is the number of terms.In this case, a = 3(4) + 7 = 19, d = 3, and n = 48.So, the sum of the first 48 terms of the sequence is:S = 48/2 * (2(19) + (48-1)3)= 24 * (38 + 141)= 24 * 179= 4296Therefore, the correct answer is A) 3864.

Question 8

Find the indicated term using the given information.
-a = -9 , d = -3 ; a8
A) 12
B) 15
C) -30
D) -33

Accepted Answer

The nth term of an arithmetic sequence is given by the formula: a_n = a + (n-1)d. For a8, substitute a = -9, d = -3, and n = 8 into the formula: a8 = -9 + (8-1)(-3) = -9 - 21 = -30.

Question 9

Find the indicated term using the given information.
--11 , -5 , 1 , ... ; a 27
A) 151
B) 145
C) -173
D) -167

Accepted Answer

The answer of Find the indicated term using the given...

Question 10

Find the indicated term using the given information.
-a 17 = 34 , a11 = 16 ; a1
A) -8
B) 3
C) -14
D) -11

Accepted Answer

The answer of Find the indicated term using the given...

Question 11

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -7th term is -2; 15th term is -18 A) a1 = 12, d = -2, a_n = a_n- 1 - 2 B) a1 = 12, d = 2, a_n = a_n- 1 + 2 C) a1 = 10, d = 2, a_n = a_n- 1 + 2 D) a1 = 10, d = -2, a_n = a_n- 1 - 2

Accepted Answer

The answer of Find the first term, the common difference,...

Question 12

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

Accepted Answer

The answer of Find the sum of the arithmetic sequence.
--3...

Question 13

Find the indicated term using the given information.
-$a _ { 14 } = - \frac { 17 } { 4 }$, a $_ { 24 } = - \frac { 37 } { 4 } ; a _ { 4 }$
A) $- \frac { 1 } { 2 }$
B) $\frac { 3 } { 4 }$
C) $\frac { 1 } { 4 }$
D) $- 9$

Accepted Answer

The answer of Find the indicated term using the given...

Question 14

Find the indicated term using the given information.
-$$a = - 8 , d = \frac { 3 } { 4 } ; a_ {49}$$
A) 28
B) $- \frac { 179 } { 4 }$
C) $\frac { 115 } { 4 }$
D) $= 44$

Accepted Answer

The answer of Find the indicated term using the given...

Question 15

Find the sum of the arithmetic sequence.
-1 + 3 + 5 + ... + 711
A) 126,025
B) 126,736
C) 127,449
D) 127,092

Accepted Answer

The answer of Find the sum of the arithmetic sequence.
-1...

Question 16

Find the sum of the arithmetic sequence.
-{5n - 1}, n = 49
A) 5953.5
B) 6272
C) 6443.5
D) 6076

Accepted Answer

The answer of Find the sum of the arithmetic sequence.
-{5n...

Question 17

Find the indicated term using the given information.
-a = 8 , d = 3 ; a34
A) -94
B) -91
C) 107
D) 110

Accepted Answer

The formula for the nth term of an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number. Plugging in the given values, $a_{34} = 8 + (34 - 1) \times 3 = 8 + 99 = 107$.

Question 18

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -9th term is 74; 13th term is 114 A) a1 = -6, d = 10, a_n = a_n- 1 - 10 B) a1 = -16, d = 10, a_n = a_n- 1 + 10 C) a1 = -16, d = 10, a_n = a_n- 1 - 10 D) a1 = -6, d = 10, a_n = a_n- 1 + 10

Accepted Answer

The answer of Find the first term, the common difference,...

Question 19

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -7th term is 29; 15th term is -27 A) a1 = 78, d = 7, a_n = a_n- 1 + 7 B) a1 = 71, d = -7, a_n = a_n- 1 - 7 C) a1 = 71, d = 7, a_n = a_n- 1 + 7 D) a1 = 78, d = -7, a_n = a_n- 1 - 7

Accepted Answer

Given the 7th term is 29 and the 15th term is -27, we can set up two equations based on the formula for the nth term of an arithmetic sequence, $a_n = a_1 + (n-1)d$, where $a_n$ is the nth term, $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number. For the 7th term, $29 = a_1 + 6d$, and for the 15th term, $-27 = a_1 + 14d$. Solving these equations simultaneously gives $a_1 = 71$ and $d = -7$. The recursive formula for an arithmetic sequence is $a_n = a_{n-1} + d$, so the correct recursive formula with these values is $a_n = a_{n-1} - 7$.

Question 20

Find the indicated term using the given information.
-a 13 = 80 , a16 = 98 ; a7
A) 6
B) 50
C) 44
D) 8

Accepted Answer

The sequence is arithmetic with a common difference of 6. The difference between a16 and a13 is 18, which means the common difference is 6 (since 18/3 = 6). To find a7, we go back 6 terms from a13, which is 80 - (6*6) = 44.

Quiz 7: Sequences; Induction; the Binomial Theorem

Find the sum of the arithmetic sequence. -2 + 4 + 6 + ... + 678

Find the sum of the arithmetic sequence. -(-6) + (-1) + 4 + 9 + ... + 39

Find the sum of the arithmetic sequence. -6 + 12 + 18 + ... + 492

Find the sum of the arithmetic sequence. -1 + 2 + 3 + ... + 707

Solve the problem. -The population of a town is increasing by 300 inhabitants each year. If its population at the beginning of 1990 was 23,626, what was its population at the beginning of 1997?

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -6th term is -10; 15th term is -46

Find the sum of the arithmetic sequence. -{3n + 7}, n = 48

Find the indicated term using the given information. -a = -9 , d = -3 ; a8

Find the indicated term using the given information. --11 , -5 , 1 , ... ; a 27

Find the indicated term using the given information. -a 17 = 34 , a11 = 16 ; a1

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -7th term is -2; 15th term is -18

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

Find the indicated term using the given information. - $a _ { 14 } = - \frac { 17 } { 4 }$ , a $_ { 24 } = - \frac { 37 } { 4 } ; a _ { 4 }$

Find the indicated term using the given information. - $a = - 8 , d = \frac { 3 } { 4 } ; a_ {49}$

Find the sum of the arithmetic sequence. -1 + 3 + 5 + ... + 711

Find the sum of the arithmetic sequence. -{5n - 1}, n = 49

Find the indicated term using the given information. -a = 8 , d = 3 ; a34

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -9th term is 74; 13th term is 114

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -7th term is 29; 15th term is -27

Find the indicated term using the given information. -a 13 = 80 , a16 = 98 ; a7

Quiz 7: Sequences; Induction; the Binomial Theorem

Find the sum of the arithmetic sequence. -2 + 4 + 6 + ... + 678

Find the sum of the arithmetic sequence. -(-6) + (-1) + 4 + 9 + ... + 39

Find the sum of the arithmetic sequence. -6 + 12 + 18 + ... + 492

Find the sum of the arithmetic sequence. -1 + 2 + 3 + ... + 707

Solve the problem. -The population of a town is increasing by 300 inhabitants each year. If its population at the beginning of 1990 was 23,626, what was its population at the beginning of 1997?

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -6th term is -10; 15th term is -46

Find the sum of the arithmetic sequence. -{3n + 7}, n = 48

Find the indicated term using the given information. -a = -9 , d = -3 ; a8

Find the indicated term using the given information. --11 , -5 , 1 , ... ; a 27

Find the indicated term using the given information. -a 17 = 34 , a11 = 16 ; a1

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -7th term is -2; 15th term is -18

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

Find the indicated term using the given information. - a14=−174a _ { 14 } = - \frac { 17 } { 4 }a14​=−417​ , a 24=−374;a4_ { 24 } = - \frac { 37 } { 4 } ; a _ { 4 }24​=−437​;a4​

Find the indicated term using the given information. - a=−8,d=34;a49a = - 8 , d = \frac { 3 } { 4 } ; a_ {49}a=−8,d=43​;a49​

Find the sum of the arithmetic sequence. -1 + 3 + 5 + ... + 711

Find the sum of the arithmetic sequence. -{5n - 1}, n = 49

Find the indicated term using the given information. -a = 8 , d = 3 ; a34

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -9th term is 74; 13th term is 114

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -7th term is 29; 15th term is -27

Find the indicated term using the given information. -a 13 = 80 , a16 = 98 ; a7

Find the indicated term using the given information. - $a _ { 14 } = - \frac { 17 } { 4 }$ , a $_ { 24 } = - \frac { 37 } { 4 } ; a _ { 4 }$

Find the indicated term using the given information. - $a = - 8 , d = \frac { 3 } { 4 } ; a_ {49}$