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 + 3 a5 = 16 |
a6 = a5 + d = 16 + 3 a6 = 19 |
a7 = a6 + d = 19 + 3 a7 = 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 + 6 a5 = 42 |
a6 = a5 + d = 42 + 6 a6 = 48 |
a7 = a6 + d = 48 + 6 a7 = 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 - 4 a5 = -82 |
a6 = a5 + d = -82 + (-4) = -82 - 4 a6 = -86 |
a7 = a6 + d = -86 + (-4) = -86 -4 a7 = -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 + 9 a5 = 5 |
a6 = a5 + d = 5 + 9 a6 = 14 |
a7 = a6 + d = 14 + 9 a7 = 23 |
Hence the next three terms of the above sequence are 5, 14 and 23.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Recent Articles
-
AP Calculus AB Problems with Solutions
Dec 26, 24 07:41 AM
AP Calculus AB Problems with Solutions -
SAT Math Resources (Videos, Concepts, Worksheets and More)
Dec 23, 24 03:47 AM
SAT Math Resources (Videos, Concepts, Worksheets and More) -
Digital SAT Math Problems and Solutions (Part - 91)
Dec 23, 24 03:40 AM
Digital SAT Math Problems and Solutions (Part - 91)
