document.write( "Question 1150834: The sum of the first ten terms of a linear sequence is -60 and the sum of the first fifteen terms of the sequence is -165.find the 18th term of the sequence \n" ); document.write( "

Algebra.Com's Answer #772337 by greenestamps(13215) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Let a = first term
\n" ); document.write( "Let d = common difference

\n" ); document.write( "10th term: a+9d
\n" ); document.write( "15th term: a+14d
\n" ); document.write( "18th term: a+17d

\n" ); document.write( "Sum of first ten terms: -60 = 10 times average of first and tenth terms

\n" ); document.write( " $\"10%28%28a%2B%28a%2B9d%29%29%2F2%29=+-60\"$
\n" ); document.write( " $\"2a%2B9d+=+-12\"$ [1]

\n" ); document.write( "Sum of first 15 terms: -165 = 15 times average of first and 15th terms\n" ); document.write( " $\"15%28%28a%2B%28a%2B14d%29%29%2F2%29+=+-165\"$
\n" ); document.write( " $\"2a%2B14d+=+-22\"$ [2]

\n" ); document.write( "Subtract [1] from [2] and solve for d; then use that value in either [1] or [2] to solve for a.

\n" ); document.write( "Finally, use the values of a and d to find the 18th term.

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

\n" );