Question

Is the sum of 22 multiples of 3 always a multiple of 3?

Answer 1

Answer:

yes sum of any number of multiples of 3 is divisible by 3

PROOF :-

Let the following variables be the multiples of 3

1. 3a
2. 3b
3. 3c
4. 3d
5. 3e
6. 3f
7. 3g
8. 3h
9. 3i
10. 3j
11. 3k
12. 3l
13. 3m
14. 3n
15. 3o
16. 3p
17. 3q
18. 3r
19. 3s
20. 3t
21. 3u
22. 3v

Here I've considered 22 variable multiples of 3

Summing them up gives us

3a + 3b + 3c + 3d + 3e + 3f .............3v

Taking 3 common from each term gives us

3 ( a + b + c + d .......v )

HERE CLEARLY THE ABOVE EXPRESSION IS A MULTIPLE OF THREE AND IT IS DIVISIBLE BY 3.

HENCE WE CAN CONCLUDE THAT SUM OF 22 MULTIPLES OF 3 IS A MULTIPLE OF 3.