Arithmetic Sequences - SSAT Upper Level: Quantitative

Card 1 of 156

0

Didn't Know

0

Didn't Know

Knew It

0

1 of 2019 left

Question

Find the next term of the arithmetic sequence:

Tap to reveal answer

Answer

The common difference is . Add this to the last given term to find the next term.

← Didn't Know|Knew It →

Question

An arithmetic sequence begins as follows:

Which of the following terms is the first negative term in the sequence?

Tap to reveal answer

Answer

The common difference of the sequence is

so the th term of the sequence is

$a_{n} = 300 -2.7 (n-1)$

To find out the minimum value for which $a_{n} < 0$ , set up this inequality:

$n > 302.7 \div 2.7 \approx 112.1$

The first negative term is the one hundred thirteenth term.

← Didn't Know|Knew It →

Question

An arithmetic sequence begins as follows:

$1 \frac{1}{7}, 3 \frac{1}{4},...$

Which of the following is the first term greater than 100?

Tap to reveal answer

Answer

The common difference of the sequence is

$3 \frac{1}{4} - 1 \frac{1}{7} = 2\frac{3}{28}$

so the th term of the sequence is

$a_{n} = 1\frac{1}{7} + \left ( 2\frac{3}{28} \right ) (n-1)$

To find out the minimum value for which $a_{n} > 100$ , set up this inequality:

$1\frac{1}{7} + \left ( 2\frac{3}{28} \right ) (n-1) > 100$

$1\frac{1}{7} + \left ( 2\frac{3}{28} \right ) n -2\frac{3}{28} > 100$

$\left ( 2\frac{3}{28} \right ) n - \frac{27}{28} > 100$

$\left ( 2\frac{3}{28} \right ) n > 100 \frac{27}{28}$

$n > 100 \frac{27}{28} \div 2\frac{3}{28} = 47 \frac{54}{59}$

The correct response is the forty-eighth term.

← Didn't Know|Knew It →

Question

The angle measures of a pentagon form an arithmetic sequence. The smallest angle measures $70^{\circ }$ . What does the largest angle measure?

Tap to reveal answer

Answer

The measures of the five angles of a pentagon add up to , based on the formula .

If the measures of the five angles form an arithmetic sequence, the angles have measures increasing by a some common difference, .

Given this pattern and the total sum, we can solve for the common difference.

$70+ \left( 70+d\right )+\left( 70+2d\right )+\left( 70+3d\right )+\left( 70+4d\right ) = 540$

The greatest of the angle measures is given by .

$70+4d = 70 + (4 )(19) = 146^{\circ }$

← Didn't Know|Knew It →

Question

Find the $8^{th}$ term of the arithmetic sequence:

Tap to reveal answer

Answer

To find any term in an arithmetic sequence, use the following formula:

is the term we want to find

is the first term of the sequence

is the number of the term we want to find

is the common difference

For this sequence,

Now, plug in the information to find the value of the 8th term.

← Didn't Know|Knew It →

Question

Find the $16^{th}$ term of the following arithmetic sequence:

Tap to reveal answer

Answer

To find any term in an arithmetic sequence, use the following formula:

is the term we want to find

is the first term of the sequence

is the number of the term we want to find

is the common difference

For this sequence,

Now, plug in the information to find the value of the 16th term.

$y_{16}=100+(-6)(16-1)=100+(-6)(15)=100-90=10$

← Didn't Know|Knew It →

Question

Find the $9^{th}$ term of the following arithmetic sequence:

Tap to reveal answer

Answer

To find any term in an arithmetic sequence, use the following formula:

is the term we want to find

is the first term of the sequence

is the number of the term we want to find

is the common difference

For this sequence,

Now, plug in the information to find the value of the 9th term.

← Didn't Know|Knew It →

Question

Find the $12^{th}$ term of the following arithmetic sequence:

Tap to reveal answer

Answer

To find any term in an arithmetic sequence, use the following formula:

is the term we want to find

is the first term of the sequence

is the number of the term we want to find

is the common difference

For this sequence,

Now, plug in the information to find the value of the 12th term.

$y_{12}=-1+(12-1)(5)=-1+(11)(5)=-1+55=54$

← Didn't Know|Knew It →

Question

Find the $7^{th}$ term for the following arithmetic sequence:

Tap to reveal answer

Answer

To find any term in an arithmetic sequence, use the following formula:

is the term we want to find

is the first term of the sequence

is the number of the term we want to find

is the common difference

For this sequence,

Now, plug in the information to find the value of the 7th term.

← Didn't Know|Knew It →

Question

Find the $10^{th}$ term of the following arithmetic sequence:

Tap to reveal answer

Answer

To find any term in an arithmetic sequence, use the following formula:

is the term we want to find

is the first term of the sequence

is the number of the term we want to find

is the common difference

For this sequence,

Now, plug in the information to find the value of the 10th term.

$y_{10}=-15+(8)(10-1)=-15+(8)(9)=-15+72=57$

← Didn't Know|Knew It →

Question

Brandon is improving very quickly at math. He improves at a rate of points per test. If he scored a on his first test, on his second test, and on his third test, what score will he get on his $8^{th}$ test?

Tap to reveal answer

Answer

You should recognize this as an arithmetic sequence:

The question is asking you to find the 8th term in this particular sequence.

To find any term in an arithmetic sequence, use the following formula:

is the term we want to find

is the first term of the sequence

is the number of the term we want to find

is the common difference

Using the information given from the question,

Now, plug in the information to find the value of the 8th term.

← Didn't Know|Knew It →

Question

Julia gets better every time she plays basketball. In her first game, she scored points. In her second game, she scored points, and in her third game, she scored points. If she continues to improve her basketball skills at this same pace, how many points should she be scoring by her $12^{th}$ game?

Tap to reveal answer

Answer

You should recognize this as an arithmetic sequence:

The question is asking you to find the 12th term in this particular sequence.

To find any term in an arithmetic sequence, use the following formula:

is the term we want to find

is the first term of the sequence

is the number of the term we want to find

is the common difference

Using the information given from the question,

Now, plug in the information to find the value of the 12th term.

$y_{12}=8+(12-1)(4)=8+(11)(4)=8+44=52$

← Didn't Know|Knew It →

Question

What is the value of x in the sequence below?

Tap to reveal answer

Answer

In this sequence, each subsequent number is equal to one third of the preceding number.

One third of 11 is equal to:

$\frac{11}{3}=3\frac{2}{3}$

Therefore, the correct answer is: $3\frac{2}{3}$

← Didn't Know|Knew It →

Question

Leon makes $\$2.00$ for the first hour of work, $\$6.00$ for his second hour of work, $\$10.00$ for his third hour of work, and so on. How much will he make for his $12^{th}$ hour of work?

Tap to reveal answer

Answer

You should recognize this as an arithmetic sequence:

The question is asking you to find the 12th term in this particular sequence.

To find any term in an arithmetic sequence, use the following formula:

is the term we want to find

is the first term of the sequence

is the number of the term we want to find

is the common difference

Using the information given from the question,

Now, plug in the information to find the value of the 12th term.

$y_{12}=2+(12-1)(4)=2+(11)(4)=2+44=46$

← Didn't Know|Knew It →

Question

Find the sum of the first terms of the following arithmetic sequence:

Tap to reveal answer

Answer

To find the sum of a certain number of terms in an arithmetic sequence, use the following formula:

$\text{Sum}=\frac{n(y_1+y_n)}{2}$

the number of the terms you have

the first term of the sequence

$y_n=n^{th}$ term of the sequence

To find the sum, we need to first find the 8th term of the sequence.

To find any term in an arithmetic sequence, use the following formula:

is the term we want to find

is the first term of the sequence

is the number of the term we want to find

is the common difference

Using the information given from the question,

Now, plug in the information to find the value of the 8th term.

Now that we know the 8th term of the sequence, we can plug in that value into the equation for the sum to find what these first 8 terms add up to.

$\text{Sum}=\frac{8(-10+32)}{2}=\frac{(8)(22)}{2}=88$

← Didn't Know|Knew It →

Question

Find the sum of the first terms of the following arithmetic sequence:

Tap to reveal answer

Answer

To find the sum of a certain number of terms in an arithmetic sequence, use the following formula:

$\text{Sum}=\frac{n(y_1+y_n)}{2}$

the number of the terms you have

the first term of the sequence

$y_n=n^{th}$ term of the sequence

To find the sum, we need to first find the 9th term of the sequence.

To find any term in an arithmetic sequence, use the following formula:

is the term we want to find

is the first term of the sequence

is the number of the term we want to find

is the common difference

Using the information given from the question,

Now, plug in the information to find the value of the 9th term.

Now that we know the 9th term of the sequence, we can plug in that value into the equation for the sum to find what these first 9 terms add up to.

$\text{Sum}=\frac{9(15+(-17))}{2}=\frac{(9)(-2)}{2}=-9$

← Didn't Know|Knew It →

Question

Hunter makes $\$4.00$ for the first hour of work, $\$6.00$ for his second hour of work, $\$8.00$ for his third hour of work, and so on. How much money will he make if he works for hours?

Tap to reveal answer

Answer

The question is basically asking you to find the sum of the first terms of the following arithmetic sequence:

To find the sum of a certain number of terms in an arithmetic sequence, use the following formula:

$\text{Sum}=\frac{n(y_1+y_n)}{2}$

the number of the terms you have

the first term of the sequence

$y_n=n^{th}$ term of the sequence

To find the sum, we need to first find the 11th term of the sequence.

To find any term in an arithmetic sequence, use the following formula:

is the term we want to find

is the first term of the sequence

is the number of the term we want to find

is the common difference

Using the information given from the question,

Now, plug in the information to find the value of the 11th term.

$y_{11}=4+(11-1)(2)=4+(10)(2)=4+20=24$

Now that we know the 11th term of the sequence, we can plug in that value into the equation for the sum to find what these first 11 terms add up to.

$\text{Sum}=\frac{11(4+24)}{2}=\frac{11(28)}{2}=154$

← Didn't Know|Knew It →

Question

Find the next term of the arithmetic sequence:

Tap to reveal answer

Answer

The common difference for this sequence is . To find the next number in the sequence, add to the last given number.

← Didn't Know|Knew It →

Question

Find the next term in the following arithmetic sequence:

Tap to reveal answer

Answer

The sequence is subtracting for each term. The next term can be found by subtracting from :

← Didn't Know|Knew It →

Question

Find the next term in the following arithmetic sequence:

$\frac{9}{2}, 4, \frac{7}{2}, ?$

Tap to reveal answer

Answer

The common difference for this arithmetic sequence is $-\frac{1}{2}$ . To find the next term in the sequence, subtract that value from the last given value.

$\frac{7}{2}-\frac{1}{2}=3$

← Didn't Know|Knew It →

0

Knew It