Algebra 1 assist » Functions and Lines » order » just how to discover the next term in an arithmetic succession

In the adhering to arithmetic sequence, what is 

*
?

*


Explanation:

The question states the the succession is arithmetic, which means we discover the next number in the sequence by adding (or subtracting) a consistent term. We understand two the the values, separated by one unknown value.

You are watching: This is an example of an arithmetic series: 6 + 8 + 10 + 12 + . . . + (4 + 2n) + . . .

We recognize that 

*
 is equally much from -1 and from 13; therefore 
*
 is equal to fifty percent the distance in between these 2 values. The distance between them deserve to be discovered by including the pure values.

*

*

The consistent in the sequence is 7. From over there we can go forward or backward to discover out that 

*
.

*

*


Given the sequence below, what is the amount of the following three numbers in the sequence?

*


*


*


*


Explanation:

By acquisition the difference in between two surrounding numbers in the sequence, we can see that the usual difference rises by one every time.

*

*

*

*

*

Our following term will certainly fit the equation

*
, an interpretation that the following term need to be
*
.

After

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

Finally, ~

*
, the next term will certainly be
*
, definition that the next term must be
*

The concern asks because that the sum of the next three terms, so now we need to add them together.

*


Explanation:

First, find a sample in the sequence. Friend will an alert that each time you move from one number to the really next one, it increases by 7. That is, the difference in between one number and the following is 7. Therefore, we can add 7 come 36 and the an outcome will it is in 43. For this reason

*
.


Explanation:

*

Determine what sort of succession you have, i.e. Even if it is the sequence alters by a constant difference or a continuous ratio. You deserve to test this by feather at bag of numbers, but this sequence has a continuous difference (arithmetic sequence).

*

*

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

*


Explanation:

First, uncover the typical difference for the sequence. Subtract the very first term indigenous the 2nd term.

*

Subtract the 2nd term native the third term.

*

Subtract the third term native the fourth term.

*

To discover the next value, add 

*
 to the last given number.

*


Explanation:

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

*

Subtract the second term indigenous the 3rd term.

*

To uncover the following value, add 

*
 to the last given number.

*


Explanation:

First, uncover the usual difference for the sequence. Subtract the first term native the 2nd term.

*

Subtract the second term from the 3rd term.

*

To uncover the next value, add 

*
 to the last provided number.

*


Explanation:

First, find the typical difference because that the sequence. Subtract the very first term indigenous the second term.

*

Subtract the 2nd term indigenous the third term.

*

To discover the next value, add 

*
 to the last given number.

*


Explanation:

First, find the typical difference because that the sequence. Subtract the an initial term from the second term.

*

Subtract the second term indigenous the 3rd term.

*

Subtract the 3rd term from the fourth term.

See more: When Water Vapor Condenses, It Releases Heat Into The Surrounding Environment.

*

To discover the next value, add 

*
 to the last offered number.

*


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