To determine the sum of all multiples of 3 between 1 and 1000.

ka1leE

ka1leE

Answered question

2021-08-04

To determine the sum of all multiples of 3 between 1 and 1000

Answer & Explanation

Nola Robson

Nola Robson

Skilled2021-08-05Added 94 answers

The multiple of 3 are 3, 6, 9, 12 ..., 999.
The sequence of multiple of 3 are in an arithmetic sequence with the first term is a1=3 and the common difference is d=3.
The n-th term of the arithmetic sequence is
an=3+(n1)3
an=3+3n3
an=3n
Therefore the n-th term of the arithmetic sequence is an=3n.
When an=999,
999=3n
9993=n
333=n
Therefore the 333-th term of the arithmetic sequence is 999.
The sum of n terms of an arithmetic sequence is given by the formula
Sn=n2(a+L)
where Sn is the sum of n terms and L is the last term of the arithmetic sequence.
For the given arithmetic sequence a=3,L=999 and n=333,
S333=3332(3+999)
S333=3332×1002
S333=333×501
S333=166833
Therefore the sum of all multiples of 3 between 1 and 1000 is 166833.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?