<PRE><B>Question 1209366</B>
&lt;br&gt;
First, informally -- which can be more educational than doing the formal mathematics....&lt;br&gt;
The 38th term is 15 terms after the 23rd term, and the value of the 38th term is 1 more than the value of the 23rd term.  So the common difference in the sequence is 1/15.&lt;br&gt;
The 41st term is 3 terms after the 38th term, so the value of the 41st term is 3 times 1/15 greater than the 38th term.  3*(1/15) = 3/15 = 1/5 = 0.2; the 41st term is 3+0.2 = 3.2.&lt;br&gt;
ANSWER: 3.2&lt;br&gt;
Formally....&lt;br&gt;
if a is the first term and d is the common difference, then...&lt;br&gt;
23rd term is a+22d
38th term is a+37d&lt;br&gt;
a+37d=3
a+22d=2&lt;br&gt;
Subtract the second equation from the first&lt;br&gt;
15d=1
d=1/15&lt;br&gt;
a+22d=2
a+(22/15)=2=30/15
a=8/15&lt;br&gt;
The first term is 8/15; the common difference is 1/15.&lt;br&gt;
The 41st term is a+40d = 8/15+40/15 = 48/15 = 16/5 = 3.2&lt;br&gt;
ANSWER (again): 3.2&lt;br&gt;
Note that, if we use the standard formal textbook method for solving the problem, we have to do a lot more work (to find the first term of the sequence) than we did using an informal method.&lt;br&gt;
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