document.write( "Question 945364: sum the serie: 1+5+9+...+77 \n" ); document.write( "

Algebra.Com's Answer #576500 by josgarithmetic(39618) $\"\"$ $\"About$

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General term of the sequence, $\"1%2B4%28n-1%29\"$ for index n.
\n" ); document.write( "Which index is the term, 77?
\n" ); document.write( " $\"1%2B4%28n-1%29=77\"$
\n" ); document.write( " $\"1%2B4n-4=77\"$
\n" ); document.write( " $\"4n=77%2B4-1\"$
\n" ); document.write( " $\"4n=80\"$
\n" ); document.write( " $\"highlight_green%28n=20%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "You can avoid dealing with the formula for sum of a sequence if you use simple sense and understanding about arithmetic series.\r
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\n" ); document.write( "\n" ); document.write( "You have twenty terms. you can form ten pair of sums all equivalent to $\"FirstTerm%2BLastTerm\"$ , or $\"1%2B77=78\"$ . No term is unpaired because you have n=20, an EVEN number of terms. The sum is 78, occurring in a sum 10 times.\r
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\n" ); document.write( "\n" ); document.write( " $\"highlight%2810%2A78=highlight%28780%29%29\"$ \n" ); document.write( "

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