Question 1190794
<br>
I will assume the "100 to 300" is inclusive....<br>
For ANY set of numbers, the sum of the terms is the number of terms, multiplied by the average of the terms.<br>
For an arithmetic sequence the average of the terms is the average of the first and last terms; the number of terms is (last minus first), divided by the common difference, plus 1.<br>
(1) sum of ALL natural numbers from 100 to 300<br>
number of terms: {{{(300-100)/1+1=201}}}
average: {{{(100+300)/2=200}}}
sum: {{{201*200=40200}}}<br>
(2) sum of natural numbers from 100 to 300 that are divisible by 4<br>
(note 100 and 300 are both divisible by 4)<br>
number of terms: {{{(300-100)/4+1=51}}}
average: {{{(100+300)/2=200}}}
sum: {{{51*200=10200}}}<br>
(3) sum of natural numbers from 100 to 300 that are NOT divisible by 4<br>
{{{40200=10200=30000}}}<br>
ANSWERS:
i) 10200
ii) 30000<br>