Question 1

Evaluate the sum.
-$\sum _ { j = 5 } ^ { 12 } ( 5 j - 4 )$

Accepted Answer

The sum can be calculated directly by evaluating each term from $j = 5$ to $j = 12$ and adding them together. Alternatively, we can use the formula for the sum of an arithmetic series. Each term in the series can be expressed as $5j - 4$, which is a linear function of $j$. The series has 8 terms (from 5 to 12 inclusive). The first term, when $j = 5$, is $5(5) - 4 = 21$, and the last term, when $j = 12$, is $5(12) - 4 = 56$. The sum of an arithmetic series is given by $\frac{n}{2}(a_1 + a_n)$, where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term. Substituting the values, we get $\frac{8}{2}(21 + 56) = 4(77) = 308$.

Question 2

Evaluate the sum.
-$\sum _ { i = 3 } ^ { 14 } ( i + 7 )$

Accepted Answer

The sum can be rewritten as $\sum_{i=3}^{14} i + \sum_{i=3}^{14} 7$. The first part is the sum of integers from 3 to 14, which is $\frac{14(14+1)}{2} - \frac{2(2+1)}{2} = 105 - 3 = 102$. The second part is $7 \times 12 = 84$. Adding these gives $102 + 84 = 186$.

Question 3

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-A man earned $2500 the first year he worked. If he received a raise of $500 at the end of each year, what was his salary during the 15th year?

Accepted Answer

The salary during the 15th year can be calculated using the formula for the nth term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number. Here, $a_1 = 2500$, $d = 500$, and $n = 15$. So, $a_{15} = 2500 + (15 - 1) \times 500 = 2500 + 7000 = 9500$.

Question 4

Find a formula for the nth term of the arithmetic sequence shown in the graph.
-

Accepted Answer

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

Question 5

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-Find the sum of all the integers from 56 to 97.

Accepted Answer

The answer of Use the sequence feature of a graphing...

Question 6

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-A certain club initially has 170 members and membership increases by 9 members every month. If dues are $5/month, what is the total amount of dues collected during the first year?

Accepted Answer

The answer of Use the sequence feature of a graphing...

Question 7

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-Find the sum of all the integers from -44 to 34.

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, $a_1 = -44$, $a_n = 34$, and $n = 34 - (-44) + 1 = 79$. Plugging these values into the formula gives $S_n = \frac{79}{2}(-44 + 34) = \frac{79}{2}(-10) = -395$.

Question 8

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-John does 9 pushups on the first day of a 30-day month, and then increases the number of pushups by 3 pushups a day. How many pushups has he done by the end of the month?

Accepted Answer

The first term is 9, the common difference is 3, and there are 30 terms. The sum of the first 10 terms is 1575.

Question 9

Find a formula for the nth term of the arithmetic sequence shown in the graph.
-

Accepted Answer

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

Question 10

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-$$a _ { n } = 3.9 n + 8.96$$

Accepted Answer

The answer of Use the sequence feature of a graphing...

Question 11

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-During the first day of an epidemic 7000 people get sick, during the second day 14,000 people get sick, and so on with the number of people getting sick increasing by 7000 each day. The epidemic
Peaks after 30 days with 7000 fewer people getting sick on the 31st day than on the 30th day, and so
Forth. What is the total number of people who get sick?

Accepted Answer

The answer of Use the sequence feature of a graphing...

Question 12

Find a formula for the nth term of the arithmetic sequence shown in the graph.
-

Accepted Answer

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

Question 13

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-The beginning population of a town was 36,000. If the population decreased by 250 people per year, how many people lived in the town 15 years later?

Accepted Answer

The population decreases by 250 people each year. After 15 years, the decrease is 15 * 250 = 3750. Subtracting this from the initial population of 36,000 gives 36,000 - 3750 = 32,250.

Question 14

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-$$a _ { n } = \sqrt { 5 } n + \sqrt { 3 }$$

Accepted Answer

The correct answer is A because the sum of the first 10 terms of the arithmetic sequence is 140.304.

Question 15

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-Martin saves $3 on the first day of a 40-day period, $6 on the second day, and so on. For the next 40 days, he increases the amount saved by $6 each day (instead of $3 each day). How much will he
Have saved after 80 days?

Accepted Answer

The answer of Use the sequence feature of a graphing...

Question 16

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-A railroad bridge is built over a V-shaped canyon. If the supports are 8 feet long at each end, the center support is 264 feet long, and the supports increase in length by 2 feet with each support
(from 8 feet to 264 feet), what is the total length of all the supports?

Accepted Answer

The total length of all the supports can be found using the formula for the sum of an arithmetic series, $S_n = \frac{n}{2}(a_1 + a_n)$, where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the nth term. Here, $a_1 = 8$ feet, $a_n = 264$ feet, and the common difference $d = 2$ feet. To find $n$, we use the formula for the nth term of an arithmetic sequence, $a_n = a_1 + (n - 1)d$. Substituting $264 = 8 + (n - 1)2$, we solve for $n$ to find the number of supports. Solving, $n = 129$. Substituting back into the sum formula, $S_n = \frac{129}{2}(8 + 264)$, we get the total length as 34,824 feet.

Question 17

Evaluate the sum.
-$\sum _ { j = 800 } ^ { 5000 } j$

Accepted Answer

The answer of Evaluate the sum.
-\(\sum _ { j =...

Question 18

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-A stack of poles has 39 poles in the bottom row, 38 poles in the next row, and so on, with 6 poles in the top row. How many poles are there in the stack?

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, $a_1 = 39$, $a_n = 6$, and $n = 34$ (since the sequence goes from 39 down to 6, which is 34 terms). Plugging these values into the formula gives $S_n = \frac{34}{2}(39 + 6) = 17 \times 45 = 765$.

Question 19

Evaluate the sum.
-$\sum _ { i = 1 } ^ { 1500 } i$

Accepted Answer

The sum of the first n natural numbers is given by the formula $\frac{n(n+1)}{2}$. For n = 1500, the sum is $\frac{1500 \times 1501}{2} = 1,125,750$.

Question 20

Find a formula for the nth term of the arithmetic sequence shown in the graph.
-

Accepted Answer

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

Quiz 12: Further Topics in Algebra

Evaluate the sum. - $\sum _ { j = 5 } ^ { 12 } ( 5 j - 4 )$

Evaluate the sum. - $\sum _ { i = 3 } ^ { 14 } ( i + 7 )$

Find a formula for the nth term of the arithmetic sequence shown in the graph. - $Find a formula for the nth term of the arithmetic sequence shown in the graph. - A) a _ { n } = n + 2 B) a _ { n } = n + 1 C) a _ { n } = n - 3 D) a _ { n } = 3 - n$

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. Round to the nearest thousandth, if necessary. -Find the sum of all the integers from 56 to 97.

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. Round to the nearest thousandth, if necessary. -Find the sum of all the integers from -44 to 34.

Find a formula for the nth term of the arithmetic sequence shown in the graph. - $Find a formula for the nth term of the arithmetic sequence shown in the graph. - A) a _ { n } = n - 3 B) a _ { n } = n + 4 C) a _ { n } = n - 4 D) a _ { n } = n + 3$

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. Round to the nearest thousandth, if necessary. - $a _ { n } = 3.9 n + 8.96$

Find a formula for the nth term of the arithmetic sequence shown in the graph. - $Find a formula for the nth term of the arithmetic sequence shown in the graph. - A) a _ { n } = 4 - n B) a _ { n } = n + 2 C) a _ { n } = n - 4 D) a _ { n } = n + 3$

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. Round to the nearest thousandth, if necessary. - $a _ { n } = \sqrt { 5 } n + \sqrt { 3 }$

Evaluate the sum. - $\sum _ { j = 800 } ^ { 5000 } j$

Evaluate the sum. - $\sum _ { i = 1 } ^ { 1500 } i$

Find a formula for the nth term of the arithmetic sequence shown in the graph. - $Find a formula for the nth term of the arithmetic sequence shown in the graph. - A) a _ { n } = n + 2 B) a _ { n } = n + 1 C) a _ { n } = n - 2 D) a _ { n } = n - 1$

Quiz 12: Further Topics in Algebra

Evaluate the sum. - ∑j=512(5j−4) \sum _ { j = 5 } ^ { 12 } ( 5 j - 4 ) ∑j=512​(5j−4)

Evaluate the sum. - ∑i=314(i+7) \sum _ { i = 3 } ^ { 14 } ( i + 7 ) ∑i=314​(i+7)

Find a formula for the nth term of the arithmetic sequence shown in the graph. -

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. Round to the nearest thousandth, if necessary. -Find the sum of all the integers from 56 to 97.

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. Round to the nearest thousandth, if necessary. -Find the sum of all the integers from -44 to 34.

Find a formula for the nth term of the arithmetic sequence shown in the graph. -

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. Round to the nearest thousandth, if necessary. - an=3.9n+8.96a _ { n } = 3.9 n + 8.96an​=3.9n+8.96

Find a formula for the nth term of the arithmetic sequence shown in the graph. -

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. Round to the nearest thousandth, if necessary. - an=5n+3a _ { n } = \sqrt { 5 } n + \sqrt { 3 }an​=5​n+3​

Evaluate the sum. - ∑j=8005000j\sum _ { j = 800 } ^ { 5000 } j∑j=8005000​j

Evaluate the sum. - ∑i=11500i\sum _ { i = 1 } ^ { 1500 } i∑i=11500​i

Find a formula for the nth term of the arithmetic sequence shown in the graph. -

Evaluate the sum. - $\sum _ { j = 5 } ^ { 12 } ( 5 j - 4 )$

Evaluate the sum. - $\sum _ { i = 3 } ^ { 14 } ( i + 7 )$

Find a formula for the nth term of the arithmetic sequence shown in the graph. - $Find a formula for the nth term of the arithmetic sequence shown in the graph. - A) a _ { n } = n + 2 B) a _ { n } = n + 1 C) a _ { n } = n - 3 D) a _ { n } = 3 - n$

Find a formula for the nth term of the arithmetic sequence shown in the graph. - $Find a formula for the nth term of the arithmetic sequence shown in the graph. - A) a _ { n } = n - 3 B) a _ { n } = n + 4 C) a _ { n } = n - 4 D) a _ { n } = n + 3$

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. Round to the nearest thousandth, if necessary. - $a _ { n } = 3.9 n + 8.96$

Find a formula for the nth term of the arithmetic sequence shown in the graph. - $Find a formula for the nth term of the arithmetic sequence shown in the graph. - A) a _ { n } = 4 - n B) a _ { n } = n + 2 C) a _ { n } = n - 4 D) a _ { n } = n + 3$

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. Round to the nearest thousandth, if necessary. - $a _ { n } = \sqrt { 5 } n + \sqrt { 3 }$

Evaluate the sum. - $\sum _ { j = 800 } ^ { 5000 } j$

Evaluate the sum. - $\sum _ { i = 1 } ^ { 1500 } i$

Find a formula for the nth term of the arithmetic sequence shown in the graph. - $Find a formula for the nth term of the arithmetic sequence shown in the graph. - A) a _ { n } = n + 2 B) a _ { n } = n + 1 C) a _ { n } = n - 2 D) a _ { n } = n - 1$