Given :
A sequence of numbers begins at 400.
To Find :
If the pattern increases by consecutive multiples of 5 starting with 5, then find the next 3 numbers in the sequence 400, ___, ___, ___ .
Solution :
This is the a question of arithmetic progression .
The first term is , a = 400 .
Now , it is given that the next numbers increase by the multiples of 5 starting with 5 .
So , common difference is , d = 5 .
Now , we know , number in A.P is given by :
Putting value of n = 2 , 3 , 4 .
We get :
Therefore , the next 3 numbers in the sequence is 400 , 405 , 410 , 415 .
Hence , this is the required solution .