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 = a_{2} - a_{1}
Step 2 :
Add the value of 'd' to each term to generate the next term.
For example, if a_{1}, a_{2}, a_{3} are in arithmetic sequence, you can add 'd' to a_{3} to generate a_{4} and so on.
That is,
a_{4} + d = a_{5}
a_{5} + d = a_{6}
a_{6} + d = a_{7}
Example 1 :
Find the next three terms of each arithmetic sequence.
4, 7, 10, 13, …
Solution :
Common difference :
d = a_{2} - a_{1}
= 7 - 4
= 3
In order to get 5^{th} term, we have to add the common difference 3 with the 4^{th} term.
a_{5} = a_{4} + d = 13 + 3 a_{5 }= 16 |
a_{6} = a_{5} + d = 16 + 3 a_{6 }= 19 |
a_{7} = a_{6} + d = 19 + 3 a_{7 }= 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 = a_{2} - a_{1}
= 24 - 18
= 6
In order to get 5^{th} term, we have to add the common difference 3 with the 4^{th} term.
a_{5} = a_{4} + d = 36 + 6 a_{5 }= 42 |
a_{6} = a_{5} + d = 42 + 6 a_{6 }= 48 |
a_{7} = a_{6} + d = 48 + 6 a_{7 }= 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 = a_{2} - a_{1}
= -70 - (-66)
= -70 + 66
= -4
In order to get 5^{th} term, we have to add the common difference 3 with the 4^{th} term.
a_{5} = a_{4} + d = -78 + (-4) _{ }= -78 - 4 a_{5 }= -82 |
a_{6} = a_{5} + d = -82 + (-4) _{ }= -82 - 4 a_{6 }= -86 |
a_{7} = a_{6} + d = -86 + (-4) = -86 -4 a_{7 }= -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 = a_{2} - a_{1}
= -22 - (-31)
= -22 + 31
= 9
In order to get 5^{th} term, we have to add the common difference 3 with the 4^{th} term.
a_{5} = a_{4} + d = -4 + 9 a_{5 }_{ }= 5 |
a_{6} = a_{5} + d = 5 + 9 a_{6 }_{ }= 14 |
a_{7} = a_{6} + d = 14 + 9 a_{7 }= 23 |
Hence the next three terms of the above sequence are 5, 14 and 23.
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