Advertisement Remove all ads

nth Term of an AP

Advertisement Remove all ads

Topics

description

  • general term of the AP

notes

nth term of an AP is also known as last term or general term. 
Let a be the first term of an AP and d be the common difference then a standard form of an AP will be a, a+d, a+2d, a+3d,............. and so on upto nth term.
In an AP terms can also be written as `a_1, a_2, a_3, a_4,........, a_n`
`a_1= a+ (1-1)d`
`a_2= a+d= a+ (2-1)d`
`a_3= a+2d=  a+ (3-1)d`
`a_4= a+3d= a+ (4-1)d`
And so on...
So if we generalize this pattern we get
`a_n= a+ (n-1)d`
Example- In an AP 2, 7, 12, ........... Then find a20
`a= 2, n=20, d= a_2-a_1= 7-2= 5`
`a_20= 2+ (20-1)5`
       = `2+ 19(5)`
       = `2+ 95`
`a_20= 97`
Now, what will do if we are asked find nth term form the end? So, we will use a different approch.
Let a be the first term of an AP and d be the common difference then a standard form of an AP will be `a, a+d, a+2d, a+3d, ......, l ` where `l` is a last term.
If the last term is `l` then the term before l will be `l-d`, and if the second last term is `l-d` then `l-d-d`  i.e `l-2d` will be the term before it and so on.
First term from the end`= l= l- (1-1)d`
Second term from the end`= l-d= l- (2-1)d`
Third term form the end`= l-2d= l- (3-1)d`
And so on...
So if we generalize this pattern we get
nth term from the end= `l- (n-1)d`
Example- 4, 9, 14, ....., 254 Find the 10th term from the end
`a= 4, n=10, d= a_2-a_1= 9-4= 5, l=254`
nth term from the end=` l- (n-1)d`
10th term from the end= `254- (10-1)5`
                                      = `254- (9)5`
                                      = `254-45`
10th term from the end= `209`

If you would like to contribute notes or other learning material, please submit them using the button below.
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×