document.write( "Question 1190794: Find the sum of all-natural numbers from 100 to 300:
\n" ); document.write( "i) Which are exactly divisible by 4.
\n" ); document.write( "ii) Excluding those which are divisible by 4. \n" ); document.write( "

Algebra.Com's Answer #822511 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "I will assume the \"100 to 300\" is inclusive....

\n" ); document.write( "For ANY set of numbers, the sum of the terms is the number of terms, multiplied by the average of the terms.

\n" ); document.write( "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.

\n" ); document.write( "(1) sum of ALL natural numbers from 100 to 300

\n" ); document.write( "number of terms: $\"%28300-100%29%2F1%2B1=201\"$
\n" ); document.write( "average: $\"%28100%2B300%29%2F2=200\"$
\n" ); document.write( "sum: $\"201%2A200=40200\"$

\n" ); document.write( "(2) sum of natural numbers from 100 to 300 that are divisible by 4

\n" ); document.write( "(note 100 and 300 are both divisible by 4)

\n" ); document.write( "number of terms: $\"%28300-100%29%2F4%2B1=51\"$
\n" ); document.write( "average: $\"%28100%2B300%29%2F2=200\"$
\n" ); document.write( "sum: $\"51%2A200=10200\"$

\n" ); document.write( "(3) sum of natural numbers from 100 to 300 that are NOT divisible by 4

\n" ); document.write( " $\"40200=10200=30000\"$

\n" ); document.write( "ANSWERS:
\n" ); document.write( "i) 10200
\n" ); document.write( "ii) 30000

\n" ); document.write( " \n" ); document.write( "

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