# Find the Sum of All Positive Multiples of 3 Less Than 50

1. 400
2. 404
3. 408
4. 412
Tahir Lecturer Asked on 9th July 2015 in

Positive multiple of 3 less than 50 are: 3,6,9,12,15,18,………,48.
The above sequence of numbers denotes as Arithmetic Progression , in which  ‘a‘ is first term of an A.P  a=3, ‘d’ is the common difference between the next and previous term of an A.P, and ‘n’ denotes the number of terms in the A.P, and ‘Sn’ denotes the sum of sequence up to nth  term . so
a=3 ,
d=6-3,9-6,12-9,……,48-45=3 ,
n=16,
Formula for finding the sum of the sequence of an A.P
Sn = n/2[2a+(n-1)d]
Sn = 16/2[2*3+(16-1)3]
Sn = 16/2[
6+15*3]
Sn = 16/2[6+45]
Sn = 8*51
Sn = 408
Hence, the sum of all positive multiples of 3 less than 50 is 408.

vijay Professor Answered on 12th July 2015.