Question 314469
The sum of all of the integers from 1 to 30 is 465. The sum of all of the integers from 1 to 30 that are divisible by 3 is 
<pre><b>
3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30 = 165, choice (D)

or do it by the formula for the sum of an arithmetic series,

with first term = {{{a[1]=3}}}, common difference {{{d= 3}}}, nth term = {{{a[n]=30}}}

{{{a[n] = a[1] + (n-1)*3}}}

{{{30 = 3 + (n-1)*3}}}

{{{27 = (n-1)*3}}}

{{{27/3 = ((n-1)*3)/3}}}

{{{9 = n-1}}}

{{{10=n}}}

Then use the sum formula:

{{{S[n]=(n/2)(a[1]+a[n])}}}

{{{S[10]=(10/2)(3+30)}}}

{{{S[10]=(5)(33)}}}

{{{S[10]=165}}}, choice (D)

Edwin</pre>