Question 1209375
<br>
Since the sequence a_1, a_2, a_3, ..., a_10 is arithmetic, the sequences<br>
[1] a_1, a_3, a_5<br>
and<br>
[2] a_2, a_4<br>
are also both arithmetic.<br>
In [1], a_3 is the middle term of the three, so it is the average of the three terms; since a_1 + a_3 + a_5 = 5, a_3 must be 5/3.<br>
But in [2], a_3 is halfway between a_2 and a_4, so a_3 must be the average of a_2 and a_4.  And a_2 + a_4 = -2, which means a_3 must be -2/2 = -1.<br>
So the conditions of the problem require that a_3 be both 5/3 and -1, which is a contradiction.<br>
ANSWER: The problem is faulty<br>