Evaluate the sum of all integers from 4 to 1000 (4 and 1000 included) excluding all multiples of both 3 and 7.(adsbygoogle = window.adsbygoogle || []).push({});

What i did was,

[tex] \sum_{r=4}^{996} r=\sum_{r=1}^{1000} r - \sum_{r=1}^{4} r [/tex]

Well, the hard part was excluding multiples of both 3 and 7. The sequence of these numbers would be,

[tex] 21, 42, 63,...n [/tex]

But however, i find no common ratio even between the 1st 3 terms. So, it is not a geometric progression. How do I evaluate a series of terms whose multiples are both 3 and 7 if they are not APs or GPs?

Thanks alot.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Simple Series Question.

**Physics Forums | Science Articles, Homework Help, Discussion**