document.write( "Question 549647: In the arithmetic Sequence, the 11th term is 72(t(11)=72), and the 27th term is 96 (t(27)=96).
\n" ); document.write( "A) Find the common Difference (generator).
\n" ); document.write( "B)Find the initial Value, t(0).
\n" ); document.write( "C) Write the rule for this sequence. \n" ); document.write( "

Algebra.Com's Answer #358161 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
The trouble here is that if your 11th term is t(11)=72, your \"initial value t(0) is really your 0th term. I call the 11th term $\"a%5B11%5D\"$ , the first term $\"a%5B1%5D\"$ , and I do not acknowledge the existence of an initial value, or term number 0. I'll have to translate my thinking to your way of naming things.
\n" ); document.write( "In your way of naming terms:
\n" ); document.write( "The common difference is $\"d\"$ .
\n" ); document.write( "There is an initial value $\"t%280%29\"$ , but
\n" ); document.write( "the first term is $\"t%281%29=t%280%29%2Bd\"$ .
\n" ); document.write( "The second term is

.
\n" ); document.write( "The n-th term is $\"t%28n%29=t%280%29%2Bnd\"$ .
\n" ); document.write( "The 11th term is $\"t%2811%29=t%280%29%2B11d=72\"$ .
\n" ); document.write( "The 27th term is $\"t%2827%29=t%280%29%2B27d=96\"$ .
\n" ); document.write( "So $\"t%2827%29-t%2811%29=t%280%29%2B27d-%28t%280%29%2B11d%29=t%280%29%2B27d-t%280%29-11d=16d\"$ .
\n" ); document.write( "But $\"t%2827%29-t%2811%29=96-72=24\"$ ,
\n" ); document.write( "so $\"16d=24\"$ --> $\"d=24%2F16=3%2F2\"$
\n" ); document.write( "The common difference is $\"3%2F2=1%261%2F2\"$ , and
\n" ); document.write( " $\"t%2811%29=t%280%29%2B11d=t%280%29%2B11%2A%283%2F2%29=72\"$ .
\n" ); document.write( "So, $\"t%280%29%2B11%2A%283%2F2%29=72\"$ --> $\"t%280%29=72-11%2A%283%2F2%29=72-33%2F2=144%2F2-33%2F2=111%2F2=55%261%2F2\"$
\n" ); document.write( "(And the first term is $\"t%281%29=t%280%29%2Bd=55%261%2F2%2B1%261%2F2=57\"$ ).
\n" ); document.write( "JUST IN CASE someone whats to read this in my language
\n" ); document.write( "In my way of naming terms:
\n" ); document.write( "The common difference is $\"d\"$ .
\n" ); document.write( "The first term is $\"a%5B1%5D\"$ .
\n" ); document.write( "The second term is $\"a%5B2%5D=a%5B1%5D%2Bd\"$ .
\n" ); document.write( "The third term is $\"a%5B3%5D=a%5B2%5D%2Bd=a%5B1%5D%2B2d\"$ .
\n" ); document.write( "The n-th term is $\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"$ .
\n" ); document.write( "The 11th term is $\"a%5B11%5D=a%5B1%5D%2B10d=72\"$ .
\n" ); document.write( "The 27th term is $\"a%5B27%5D=a%5B1%5D%2B26d=96\"$ .
\n" ); document.write( "So $\"a%5B27%5D-a%5B11%5D=a%5B1%5D%2B26d-%28a%5B1%5D%2B10d%29=a%5B1%5D%2B26d-a%5B1%5D-10d=16d\"$ .
\n" ); document.write( "But $\"a%5B27%5D-a%5B11%5D=96-72=24\"$ ,
\n" ); document.write( "so $\"16d=24\"$ --> $\"d=24%2F16=3%2F2\"$
\n" ); document.write( "The common difference is $\"3%2F2\"$
\n" ); document.write( "and $\"a%5B11%5D=a%5B1%5D%2B10d=a%5B1%5D%2B10%2A%283%2F2%29=a%5B1%5D%2B15=72\"$ --> $\"a%5B1%5D=72-15=57\"$ \n" ); document.write( "

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