document.write( "Question 1011672: How many terms in the series 5+9+13=......+tn are less than 500? How many terms are neede for a sum of less than 500? \n" ); document.write( "
Algebra.Com's Answer #627398 by Boreal(15235)\"\" \"About 
You can put this solution on YOUR website!
The series is 4n+1
\n" ); document.write( "4n+1=497 when 4n=496 and n=124.
\n" ); document.write( "There are 124 terms.
\n" ); document.write( "=====
\n" ); document.write( "sum=(n/2)(a1+an)
\n" ); document.write( "a1=5
\n" ); document.write( "a2=9
\n" ); document.write( "a3=13
\n" ); document.write( "a4=17
\n" ); document.write( "sum<500
\n" ); document.write( "500>(n/2)(5+4n+1)=(n/2)(4n+6)
\n" ); document.write( "1000>4n^2+6n
\n" ); document.write( "4n^2+6n-1000<0
\n" ); document.write( "2n^2+3n-500<0
\n" ); document.write( "n=(1/4)(-3+/- sqrt (9+4000); sqrt 4009=63.31
\n" ); document.write( "n=(1/4)(60.31)
\n" ); document.write( "n=15.07
\n" ); document.write( "so n=15 will be correct
\n" ); document.write( "n=15, term is 61
\n" ); document.write( "sum=(15/2)(5+61)=66*7.5=493
\n" ); document.write( "15 terms\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );