document.write( "Question 1202468: Calculate the sum between and including the terms t16 and t53 of an arithmetic sequence with first term 543 and common difference - 12. \n" ); document.write( "

Algebra.Com's Answer #837333 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The response from the other tutor has at least a couple of significant errors, starting with a common difference of 12 instead of -12.

\n" ); document.write( "Overlooking those errors, her presentation of the solution does little to help the student learn.

\n" ); document.write( "The sequence consisting of the 16th through 53rd terms of an arithmetic sequence is itself an arithmetic sequence.

\n" ); document.write( "The first term of that sequence (the 16th term of the original sequence) is the first term of the original sequence, plus the common difference 15 times: $\"543%2B15%28-12%29=543-180=363\"$ .

\n" ); document.write( "The last term of the new sequence ( the 53rd term of the original sequence) is the first term of the original sequence, plus the common difference 52 times: $\"543%2B52%28-12%29=543-624=-81\"$ .

\n" ); document.write( "The number of terms in the new sequence is $\"%2853-16%29%2B1=38\"$ .

\n" ); document.write( "The sum of the terms of the new sequence is the number of terms, times the average of the first and last terms: $\"38%28%28363-81%29%2F2%29=38%2A141=5358\"$ .

\n" ); document.write( "ANSWER: 5358
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