Question 1

Write out the first three terms and the last term of the arithmetic sequence.
-$$\sum _ { i = 1 } ^ { 60 } - 5 i$$
A) $- 1 - 5 - 10 - \ldots - 300$
B) $- 5 - 25 - 125 - \ldots - 1500$
C) $- 5 + 25 - 75 + \ldots - 1500$
D) $- 5 - 10 - 15 - \ldots - 300$

Accepted Answer

The given sequence is an arithmetic sequence with the first term $a_1 = -5$ and common difference $d = -5$. The $n$th term of an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$. For $n = 60$, the last term is $a_{60} = -5 + (60 - 1)(-5) = -5 - 295 = -300$. The first three terms are $-5, -10, -15$, and the last term is $-300$, matching option D.

Question 2

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
-2 , 6 , 10 , 14 , 18 , . . . 
A) $a _ { n } = 2 n - 4 ; a _ { 20 } = 36$
B) $a _ { n } = 4 n + 2 ; a _ { 20 } = 82$
C) $a _ { n } = 4 n - 2 ; a _ { 20 } = 78$
D) $a _ { n } = n + 4 ; a _ { 20 } = 24$

Accepted Answer

The sequence is arithmetic with a common difference of 4. The nth term formula is $a_n = 4n - 2$. For $a_{20}$, substitute n = 20: $a_{20} = 4(20) - 2 = 78$.

Question 3

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
-Find 1 + 3 + 5 + 7 + . . ., the sum of the first 55 positive odd integers.
A) 2970
B) 3025
C) 3029
D) 2966

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. For the given sequence, $a_1 = 1$, $n = 55$, and $a_n = 1 + 2(n-1) = 1 + 2(55-1) = 109$. Plugging these values into the formula gives $S_{55} = \frac{55}{2}(1 + 109) = \frac{55}{2}(110) = 3025$.

Question 4

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence
with the given first term, a1, and common difference, d.
-Find a 17 when a1 = -4 , d = - 1 .
A) 12
B) 13
C) - 20
D) - 21

Accepted Answer

The formula for the nth term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$. Substituting the given values, $a_{17} = -4 + (17 - 1)(-1) = -4 + 16(-1) = -4 - 16 = -20$.

Question 5

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence
with the given first term, a1, and common difference, d.
-Find a90 when a1 = -14, d = -5.
A) -464
B) 431
C) -459
D) 436

Accepted Answer

The answer of Use the formula for the general term...

Question 6

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
-$$a _ { 1 } = - \frac { 3 } { 4 } , d = \frac { 5 } { 4 }$$
A) $a _ { n } = \frac { 5 } { 4 } n - 2 ; a _ { 20 } = 23$
B) $a _ { n } = \frac { 5 } { 4 } n - \frac { 3 } { 4 } ; a _ { 20 } = \frac { 97 } { 4 }$
C) $a _ { n } = - \frac { 3 } { 4 } n + \frac { 5 } { 4 } ; a _ { 20 } = - \frac { 55 } { 4 }$
D) $a _ { n } = - \frac { 3 } { 4 } n + 2 ; a _ { 20 } = - 13$

Accepted Answer

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, $d$ is the common difference, and $n$ is the term number.Substituting the given values into the formula, we get:$$a_n = -\frac{3}{4} + (n-1)\frac{5}{4}$$$$a_n = -\frac{3}{4} + \frac{5}{4}n - \frac{5}{4}$$$$a_n = \frac{5}{4}n - 2$$To find $a_{20}$, we substitute $n=20$ into the formula:$$a_{20} = \frac{5}{4}(20) - 2$$$$a_{20} = 25 - 2$$$$a_{20} = 23$$

Question 7

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence
with the given first term, a1, and common difference, d.
-Find a11 when a1 = 20, d = -6.
A) 80
B) -46
C) -40
D) -60

Accepted Answer

The formula for the nth term of an arithmetic sequence is given by a_n = a1 + (n-1)d. Substituting the given values: a11 = 20 + (11-1)(-6) = 20 - 60 = -40.

Question 8

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
-Find the sum of the first eight terms of the arithmetic sequence: 10, 15, 20, . . . .
A) 220
B) 45
C) 120
D) 440

Accepted Answer

The partial sum formula for an arithmetic sequence is $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the sum of the first $n$ terms, $a_1$ is the first term, and $a_n$ is the nth term. Here, $n = 8$, $a_1 = 10$, and $a_n = a_1 + (n-1)d = 10 + (8-1)5 = 45$. Thus, $S_8 = \frac{8}{2}(10 + 45) = 4 \times 55 = 220$.

Question 9

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
--21, -26 , -31, -36, . . . 
A) $a _ { n } = 5 n + 16 ; a _ { 20 } = 116$
B) $a _ { n } = 5 n + 21 ; a _ { 20 } = 121$
C) $a _ { n } = - 5 n - 16 ; a _ { 20 } = - 116$
D) $a _ { n } = - 5 n - 21 ; a _ { 20 } = - 121$

Accepted Answer

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

Question 10

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
-Find the sum of the first four terms of the arithmetic sequence: -3, -15, -27, . . . .
A) 84
B) -60
C) - 84
D) -45

Accepted Answer

The formula for the sum of the first n terms of an arithmetic sequence is $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the sum of the first n terms, $a_1$ is the first term, and $a_n$ is the nth term. Here, $n = 4$, $a_1 = -3$, and the common difference $d = -12$. The fourth term $a_4 = a_1 + 3d = -3 + 3(-12) = -3 - 36 = -39$. Thus, $S_4 = \frac{4}{2}(-3 - 39) = 2(-42) = -84$.

Question 11

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
-27, 18 , 9, 0, . . . 
A) $a _ { n } = 27 - 9 n ; a _ { 20 } = - 153$
B) $a _ { n } = 36 - 9 n ; a _ { 20 } = - 144$
C) $a _ { n } = 9 n - 27 ; a _ { 20 } = 153$
D) $a _ { n } = 9 n - 36 ; a _ { 20 } = 144$

Accepted Answer

The sequence is arithmetic with the first term $a_1 = 27$ and a common difference $d = 18 - 27 = -9$. The formula for the nth term is $a_n = a_1 + (n-1)d = 27 + (n-1)(-9) = 36 - 9n$. For $a_{20}$, substitute $n = 20$: $a_{20} = 36 - 9(20) = -144$.

Question 12

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence
with the given first term, a1, and common difference, d.
-Find a 32 when a1 = -3 , d = 3 .
A) 93
B) -96
C) -99
D) 90

Accepted Answer

The answer of Use the formula for the general term...

Question 13

Solve the problem.
-To train for a race, Will begins by jogging 11 minutes one day per week. He increases his jogging time by 3 minutes each week. Write the general term of this arithmetic sequence, and find how many weeks it takes for
Him to reach a jogging time of one hour. 
A) $a _ { n } = 3 n + 11 ; 18$ weeks
B) $a _ { n } = 3 n + 11 ; 17$ weeks
C) $a _ { n } = 3 n + 8 ; 18$ weeks
D) $a _ { n } = 3 n + 8 ; 17$ weeks

Accepted Answer

The answer of Solve the problem.
-To train for a race,...

Question 14

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
-Find the sum of the first 70 terms of the arithmetic sequence: 1, 8, 15, 22, . . . .
A) 16,733
B) 15,990
C) 17,220
D) 16,975

Accepted Answer

The answer of Use the partial sum formula to find...

Question 15

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence
with the given first term, a1, and common difference, d.
-Find a8 when a1 = -8 , d = -5 .
A) -43
B) 27
C) -48
D) 32

Accepted Answer

The formula for the nth term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$. Substituting $a_1 = -8$, $d = -5$, and $n = 8$, we get $a_8 = -8 + (8 - 1)(-5) = -8 - 35 = -43$.

Question 16

Solve the problem.
-Jacie is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of $130 during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at
The end of her first year. 
A) $a _ { n } = 2870 + 130 n ; \$ 4430$
B) $a _ { n } = 3000 + 130 n ; \$ 4560$
C) $a _ { n } = 3000 + 130 n ; \$ 4430$
D) $a _ { n } = 2870 + 130 ( n - 1 ) ; \$ 4300$

Accepted Answer

The general 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. Here, $a_1 = 3000$ and $d = 130$, so the general term is $a_n = 3000 + (n - 1)130$. However, the correct formula should adjust the starting point to align with the sequence's progression, making $a_n = 2870 + 130n$ a better fit, considering the sequence's structure. For the salary at the end of the first year (12th month), it should be $a_{12} = 2870 + 130 \times 12 = 4430$, which matches option A.

Question 17

Solve the problem.
-The population of a town is increasing by 400 inhabitants each year. If its current population is 29,089 and this trend continues, what would its population be in 8 years?
A) 232,600 inhabitants
B) 32,289 inhabitants
C) 465,200 inhabitants
D) 31,889 inhabitants

Accepted Answer

The population increases by 400 inhabitants each year. In 8 years, the increase will be 8 * 400 = 3,200. Adding this to the current population of 29,089 gives 29,089 + 3,200 = 31,889 inhabitants.

Question 18

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
-$$a _ { 1 } = - 7 , d = 0.5$$
A) $a _ { n } = - 7 n + 7.5 ; a _ { 20 } = - 132.5$
B) $a _ { n } = - 7 n + 0.5 ; a _ { 20 } = - 139.5$
C) $a _ { n } = 0.5 n - 7 ; a _ { 20 } = 3$
D) $a _ { n } = 0.5 n - 7.5 ; a _ { 20 } = 2.5$

Accepted Answer

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 $a_1 = -7$ and $d = 0.5$ gives $a_n = -7 + (n - 1)(0.5) = -7 + 0.5n - 0.5 = 0.5n - 7.5$. For $n = 20$, $a_{20} = 0.5(20) - 7.5 = 10 - 7.5 = 2.5$.

Question 19

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
-Find the sum of the odd integers between 24 and 66.
A) 900
B) 990
C) 945
D) 1035

Accepted Answer

The odd integers between 24 and 66 are 25, 27, ..., 65. This is an arithmetic sequence with the first term a = 25, the last term l = 65, and the common difference d = 2. The number of terms n can be found using the formula n = (l - a)/d + 1 = (65 - 25)/2 + 1 = 21. The partial sum S_n of an arithmetic sequence is given by S_n = n/2 * (a + l). Substituting the values, S_21 = 21/2 * (25 + 65) = 21/2 * 90 = 945.

Question 20

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
-3 , 12 , 21 , 30 , 39 , . . . 
A) $a _ { n } = 6 n - 2 ; a _ { 20 } = 118$
B) $a _ { n } = 9 n - 2 ; a _ { 20 } = 178$
C) $a _ { n } = 6 n - 9 ; a _ { 20 } = 111$
D) $a _ { n } = 9 n - 6 ; a _ { 20 } = 174$

Accepted Answer

The common difference (d) is 9 (12 - 3 = 9). The first term (a1) is 3. The formula for the nth term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$. Substituting the values, we get $a_n = 3 + (n - 1)9 = 9n - 6$. For the 20th term, $a_{20} = 9(20) - 6 = 180 - 6 = 174$.

Quiz 10: Radicals, Radical Functions, and Rational Exponents

Write out the first three terms and the last term of the arithmetic sequence. - $\sum _ { i = 1 } ^ { 60 } - 5 i$

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20, the 20th term of the sequence. -2 , 6 , 10 , 14 , 18 , . . .

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find 1 + 3 + 5 + 7 + . . ., the sum of the first 55 positive odd integers.

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a 17 when a1 = -4 , d = - 1 .

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a90 when a1 = -14, d = -5.

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20, the 20th term of the sequence. - $a _ { 1 } = - \frac { 3 } { 4 } , d = \frac { 5 } { 4 }$

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a11 when a1 = 20, d = -6.

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find the sum of the first eight terms of the arithmetic sequence: 10, 15, 20, . . . .

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20, the 20th term of the sequence. --21, -26 , -31, -36, . . .

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find the sum of the first four terms of the arithmetic sequence: -3, -15, -27, . . . .

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20, the 20th term of the sequence. -27, 18 , 9, 0, . . .

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a 32 when a1 = -3 , d = 3 .

Solve the problem. -To train for a race, Will begins by jogging 11 minutes one day per week. He increases his jogging time by 3 minutes each week. Write the general term of this arithmetic sequence, and find how many weeks it takes for Him to reach a jogging time of one hour.

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find the sum of the first 70 terms of the arithmetic sequence: 1, 8, 15, 22, . . . .

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a8 when a1 = -8 , d = -5 .

Solve the problem. -Jacie is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of $130 during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at The end of her first year.

Solve the problem. -The population of a town is increasing by 400 inhabitants each year. If its current population is 29,089 and this trend continues, what would its population be in 8 years?

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20, the 20th term of the sequence. - $a _ { 1 } = - 7 , d = 0.5$

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find the sum of the odd integers between 24 and 66.

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20, the 20th term of the sequence. -3 , 12 , 21 , 30 , 39 , . . .