# HOW TO FIND THE NEXT THREE TERMS IN ARITHMETIC SEQUENCE

The following steps will be useful to find the next three terms in an arithmetic sequence.

Step 1 :

Using the given terms, find the common difference.

Formula to find common difference 'd' :

d  =  a2 - a1

Step 2 :

Add the value of 'd' to each term to generate the next term.

For example, if a1, a2, a3 are in arithmetic sequence, you can add 'd' to a3 to generate a4 and so on.

That is,

a4 + d = a5

a5 + d = a6

a6 + d = a7

Example 1 :

Find the next three terms of each arithmetic sequence.

4, 7, 10, 13, …

Solution :

Common difference :

d  =  a2 - a1

=  7 - 4

=  3

In order to get 5th term, we have to add the common difference 3 with the 4th term.

 a5  =  a4 + d=  13 + 3a5 =  16 a6  =  a5 + d=  16 + 3a6 =  19 a7  =  a6 + d=  19 + 3a7 =  21

Hence the next three terms of the above sequence are 16, 19 and 21.

Example 2 :

Find the next three terms of each arithmetic sequence.

18, 24, 30, 36, …

Solution :

Common difference :

d  =  a2 - a1

=  24 - 18

=  6

In order to get 5th term, we have to add the common difference 3 with the 4th term.

 a5  =  a4 + d=  36 + 6a5 =  42 a6  =  a5 + d=  42 + 6a6 =  48 a7  =  a6 + d=  48 + 6a7 =  54

Hence the next three terms of the above sequence are 42, 48 and 54.

Example 3 :

Find the next three terms of each arithmetic sequence.

-66, -70, -74, -78, …

Solution :

Common difference :

d  =  a2 - a1

=  -70 - (-66)

=  -70 + 66

=  -4

In order to get 5th term, we have to add the common difference 3 with the 4th term.

 a5  =  a4 + d=  -78 + (-4) =  -78 - 4a5  =  -82 a6  =  a5 + d=  -82 + (-4) =  -82 - 4a6  =  -86 a7  =  a6 + d= -86 + (-4)= -86 -4a7 =  -90

Hence the next three terms of the above sequence are -82, -86, and -90.

Example 4 :

Find the next three terms of each arithmetic sequence.

-31, -22, -13, -4, …

Solution :

Common difference :

d  =  a2 - a1

=  -22 - (-31)

=  -22 + 31

=  9

In order to get 5th term, we have to add the common difference 3 with the 4th term.

 a5  =  a4 + d=  -4 + 9a5  =  5 a6  =  a5 + d=  5 + 9a6  =  14 a7  =  a6 + d=  14 + 9a7 = 23

Hence the next three terms of the above sequence are 5, 14 and 23.

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