document.write( "Question 1003573: Find the number of terms in the following arithmetic sequence.
\n" ); document.write( "8,11,14,17,...41 \n" ); document.write( "

Algebra.Com's Answer #620268 by KMST(5328) $\"\"$ $\"About$

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Each term is $\"3\"$ more than the one before.
\n" ); document.write( " $\"11-8=3\"$ , $\"14-11=3\"$ , etc.\r
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\n" ); document.write( "\n" ); document.write( "MENTAL MATH:
\n" ); document.write( "The difference between the last term an the second term is
\n" ); document.write( " $\"41-11=30=3%2A10\"$ .
\n" ); document.write( "That means that after $\"11\"$ , $\"3\"$ was added $\"10\"$ times,
\n" ); document.write( "meaning that there are $\"10\"$ terms after $\"11\"$ .
\n" ); document.write( "Since $\"11\"$ is term number $\"2\"$ ,
\n" ); document.write( "there are $\"2%2B10=highlight%2812%29\"$ terms.\r
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\n" ); document.write( "\n" ); document.write( "FORMULA-HAPPY:
\n" ); document.write( "Since each term is $\"3\"$ more that the one before,
\n" ); document.write( "the common difference for this arithmetic sequence is $\"d=3\"$ .
\n" ); document.write( "The first tern is $\"a%5B1%5D=8\"$ .
\n" ); document.write( "In an arithmetic sequence, term number $\"n\"$ is
\n" ); document.write( " $\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad\"$ .
\n" ); document.write( "In this arithmetic sequence, term number $\"n\"$ is
\n" ); document.write( " $\"a%5Bn%5D=8%2B3%28n-1%29\"$ .
\n" ); document.write( "We want to know what is the term number $\"n\"$ for the last term, $\"41\"$ .
\n" ); document.write( "So we write,
\n" ); document.write( " $\"8%2B3%28n-1%29=41\"$ , and solve for $\"n\"$ :
\n" ); document.write( " $\"8%2B3%28n-1%29=41\"$ --> $\"3%28n-1%29=41-8\"$ --> $\"3%28n-1%29=33\"$ --> $\"n-1=33%2F3\"$ --> $\"n-1=11\"$ --> $\"n=11%2B1\"$ --> $\"highlight%28n=12%29\"$ . \n" ); document.write( "

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