Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #10 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the following arithmetic sequence: 

Possible Answers:

Correct answer:

Explanation:

First, find the common difference for the sequence. Subtract the first term from the second term.

Subtract the second term from the third term.

Subtract the third term from the fourth term.

To find the next value, add  to the last given number.

Example Question #11 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the following arithmetic sequence:

Possible Answers:

Correct answer:

Explanation:

First, find the common difference for the sequence. Subtract the first term from the second term.

Subtract the second term from the third term.

To find the next value, add  to the last given number.

Example Question #191 : Functions And Lines

Find the next term in the following arithmetic sequence:

Possible Answers:

Correct answer:

Explanation:

First, find the common difference for the sequence. Subtract the first term from the second term.

Subtract the second term from the third term.

To find the next value, add  to the last given number.

Example Question #13 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the arithmetic sequence:

Possible Answers:

Correct answer:

Explanation:

First, find the common difference for the sequence. Subtract the first term from the second term.

Subtract the second term from the third term.

To find the next value, add  to the last given number.

Example Question #14 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the given arithmetic sequence:

Possible Answers:

Correct answer:

Explanation:

First, find the common difference for the sequence. Subtract the first term from the second term.

Subtract the second term from the third term.

To find the next value, add  to the last given number.

Example Question #15 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the following arithmetic sequence:

Possible Answers:

Correct answer:

Explanation:

First, find the common difference for the sequence. Subtract the first term from the second term.

Subtract the second term from the third term.

To find the next value, add  to the last given number.

Example Question #16 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the arithmetic sequence:  

Possible Answers:

Correct answer:

Explanation:

The terms are in decreasing order, and to determine how much each number is decreasing by, we will subtract first term with the second term and the second term with the third term.

Subtract the first and second term.

Subtract the second and the third term.

Notice that each term is subtracted by five.

Subtract the third term by five to get the next term.

The answer is .

Example Question #12 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the following sequence.

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

The two things we need to find out are HOW the sequence changes (adddition, subtraction, multiplication, division, etc.) and by WHAT factor.

Start by finding the difference between the first two terms.

Now let's find the difference between the 2nd and 3rd given term.

Based on these two points, we can infer that this sequence changes by adding 13 to the previous term. Therefore...

the next term in the sequence is 22.

Example Question #1 : How To Find Direct Variation

If an object is hung on a spring, the elongation of the spring varies directly as the mass of the object. A 20 kg object increases the length of a spring by exactly 7.2 cm. To the nearest tenth of a centimeter, by how much does a 32 kg object increase the length of the same spring?

Possible Answers:

Correct answer:

Explanation:

Let  be the mass of the weight and the elongation of the spring. Then for some constant of variation 

We can find  by setting  from the first situation:

so 

In the second situation, we set  and solve for :

 

which rounds to 11.5 centimeters.

Example Question #1 : How To Find Direct Variation

 varies directly with the square root of . If , then  . What is the value of  if ?

Possible Answers:

None of these answers are correct.

Correct answer:

Explanation:

If  varies directly with the square root of , then for some constant of variation

If , then ; therefore, the equation becomes 

or

.

Divide by 5 to get , making the equation 

.

If , then .

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