Advertisement

General Term of an Arithmetic Progression

notes

In the sequence 5, 8, 11, 14, . . . the difference between two consecutive terms is 3.
Hence, this sequence is an A.P.
Here the first term is 5. If 3 is added to 5 we get the second term 8. Similarly to find 100th term what should be done?

First term       Second term         Third term . . .
Number 5,     5 + 3 = 8                8 + 3 = 11 . . .
In this way reaching upto 100th term will be time consuming. Let’s see if we can find any formula for it.

Generally in the A.P. t1, t2, t3, . . . If first term is a and common difference is d,
t1= a
t2= t1+ d = a + d = a + (2 - 1) d
t3= t2+ d = a + d + d = a + 2d = a + (3 - 1)d
t4= t3+ d = a + 2d + d = a + 3d = a +(4 - 1)d
We get tn= a +(n - 1) d.

Using the above formula we can find the 100th term of the A.P. 5, 8, 11, 14, . . .
Here a = 5 d = 3
tn = a +(n - 1)d
t100= 5 +(100 - 1) × 3
= 5 + 99 × 3
= 5 + 297
t100 = 302
100th tem of this A.P. is 302.

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

View all notifications
Login
Create free account


      Forgot password?
View in app×