The formula given below can be used to write an equation for a arithmetic sequence.
an = a1 + (n - 1)d
Here, a1 stands for the first term of the given arithmetic sequence and 'd' stands for the common difference.
Formula to find common difference (d) :
d = a2 - a1
Find the nth nth term of each arithmetic sequence.
Example 1 :
-3, -6, -9, -12, ......
Solution :
In the given arithmetic sequence
a1 = -3
d = a2 - a1
= -6 - (-3)
= -6 + 3
= -3
Formula to find nth term of an arithmetic sequence :
an = a1 + (n - 1)d
Substitute a1 = -3 and d = -3.
an = -3 + (n - 1)(-3)
an = -3 - 3n + 3
an = -3n
Example 2 :
8, 9, 10, 11, ......
Solution :
In the given arithmetic sequence
a1 = 8
d = a2 - a1
= 9 - 8
= 1
Formula to find nth term of an arithmetic sequence :
an = a1 + (n - 1)d
Substitute a1 = 8 and d = 1.
an = 8 + (n - 1)(1)
an = 8 + n - 1
an = n + 7
Example 3 :
2, 8, 14, 20, ......
Solution :
In the given arithmetic sequence
a1 = 2
d = a2 - a1
= 8 - 2
= 6
Formula to find nth term of an arithmetic sequence :
an = a1 + (n - 1)d
Substitute a1 = 2 and d = 6.
an = 2 + (n - 1)(6)
an = 2 + 6n - 6
an = 6n - 4
Example 4 :
-18, -16, -14, -12, ......
Solution :
In the given arithmetic sequence
a1 = -18
d = a2 - a1
= -16 - (-18)
= -16 + 18
= 2
Formula to find nth term of an arithmetic sequence :
an = a1 + (n - 1)d
Substitute a1 = -18 and d = 2.
an = -18 + (n - 1)(2)
an = -18 + 2n - 2
an = 2n - 20
Example 5 :
12, 23, 34, 45, ......
Solution :
In the given arithmetic sequence
a1 = 23
d = a2 - a1
= 23 - 12
= 11
Formula to find nth term of an arithmetic sequence :
an = a1 + (n - 1)d
Substitute a1 = 12 and d = 11.
an = 12 + (n - 1)(11)
an = 12 + 11n - 11
an = 11n - 1
Example 6 :
9, 17, 25, 33, ......
Solution :
In the given arithmetic sequence
a1 = 9
d = a2 - a1
= 17 - 9
= 8
Formula to find nth term of an arithmetic sequence :
an = a1 + (n - 1)d
Substitute a1 = 9 and d = 8.
an = 9 + (n - 1)(8)
an = 9 + 8n - 8
an = 8n + 1
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Apr 17, 24 11:27 PM
Apr 16, 24 09:28 AM
Apr 15, 24 11:17 PM