Sequences

Help Questions

Algebra › Sequences

Questions 1 - 10
1

Find the next term in the given arithmetic sequence:

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.

2

Given the sequence below, what is the sum of the next three numbers in the sequence?

Explanation

By taking the difference between two adjacent numbers in the sequence, we can see that the common difference increases by one each time.

Our next term will fit the equation , meaning that the next term must be .

After , the next term will be , meaning that the next term must be .

Finally, after , the next term will be , meaning that the next term must be

The question asks for the sum of the next three terms, so now we need to add them together.

3

Given the sequence below, what is the sum of the next three numbers in the sequence?

Explanation

By taking the difference between two adjacent numbers in the sequence, we can see that the common difference increases by one each time.

Our next term will fit the equation , meaning that the next term must be .

After , the next term will be , meaning that the next term must be .

Finally, after , the next term will be , meaning that the next term must be

The question asks for the sum of the next three terms, so now we need to add them together.

4

Find the next term in the given arithmetic sequence:

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.

5

Find the next term in the following arithmetic sequence:

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.

6

Find the next term in the following arithmetic sequence:

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.

7

What is the common difference in the following sequence?

Explanation

What is the common difference in the following sequence?

Common differences are associated with arithematic sequences.

A common difference is the difference between consecutive numbers in an arithematic sequence. To find it, simply subtract the first term from the second term, or the second from the third, or so on...

See how each time we are adding 8 to get to the next term? This means our common difference is 8.

8

The first term of an arithmetic sequence is ; the fifth term is . What is the second term?

Explanation

To find the common difference , use the formula .

For us, is and is .

Now we can solve for .

Add the common difference to the first term to get the second term.

9

Find the next term in the following sequence.

None of the other answers.

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.

10

Find the next term in the following arithmetic sequence:

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.

Page 1 of 10