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

**Answer: 3. 408;
**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

**n**th term . s

**o**

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]

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[

**Sn = 16/2[6+45]**

**Sn = 8*51**

**Sn = 408**

Hence, the sum of all positive multiples of 3 less than 50

**is 408.**