Algebra 1 Aid » Functions and Lines » Sequences » How to discover the next term in an arithmetic sequence

In the complying with arithmetic sequence, what is 

*
?

*


Explanation:

The question says that the sequence is arithmetic, which indicates we find the next number in the sequence by adding (or subtracting) a continuous term. We know two of the worths, separated by one unwell-known value.

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We know that 

*
 is equally much from -1 and also from 13; therefore 
*
 is equal to half the distance in between these two worths. The distance in between them can be uncovered by including the absolute worths.

*

*

The continuous in the sequence is 7. From there we can go forward or backward to uncover out that 

*
.

*

*


Given the sequence below, what is the sum of the following 3 numbers in the sequence?

*


*


*


*


Explanation:

By taking the distinction in between 2 nearby numbers in the sequence, we can check out that the widespread distinction increases by one each time.

*

*

*

*

*

Our following term will certainly fit the equation

*
, meaning that the next term must be
*
.

After

*
, the next term will be
*
, definition that the next term need to be 
*
.

Finally, after

*
, the next term will be
*
, meaning that the following term have to be
*

The question asks for the amount of the following three terms, so currently we need to include them together.

*


Explanation:

First, discover a pattern in the sequence. You will alert that each time you relocate from one number to the very following one, it rises by 7. That is, the difference in between one number and the next is 7. Therefore, we can include 7 to 36 and the outcome will be 43. Therefore

*
.


Explanation:

*

Determine what sort of sequence you have, i.e. whether the sequence changes by a continuous distinction or a consistent proportion. You have the right to test this by looking at pairs of numbers, yet this sequence has a continuous distinction (arithmetic sequence).

*

*

So the sequence developments by subtracting 16 each time. Apply this to the last offered term.

*


Explanation:

First, discover the widespread difference for the sequence. Subtract the first term from the second term.

*

Subtract the second term from the third term.

*

Subtract the 3rd term from the fourth term.

*

To find the next value, add 

*
 to the last provided number.

*


Explanation:

First, find the prevalent distinction 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 provided number.

*


Explanation:

First, uncover the prevalent distinction for the sequence. Subtract the initially term from the second term.

*

Subtract the second term from the third term.

*

To uncover the next worth, add 

*
 to the last given number.

*


Explanation:

First, uncover the common difference for the sequence. Subtract the initially term from the second term.

*

Subtract the second term from the third term.

*

To uncover the next worth, add 

*
 to the last given number.

*


Explanation:

First, uncover the widespread distinction 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 following worth, add 

*
 to the last given number.

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*


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